WASHINGTON >> Determined to defy the stereotype of a weakened short-timer, President Barack Obama is ending 2015 with a series of accomplishments, most notably a nuclear agreement with Iran, an international climate accord, a 12-nation Pacific trade pact, and long-stalled deals on the budget, education and transportation.

But as he begins his final year in office, those achievements have been overshadowed by Americans’ anxiety over terror attacks and the expanding battle with the Islamic State, along with a public perception that Obama is unable or unwilling to channel the nation’s fears.

Obama has the lowest rating of his presidency for terrorism, with 37 percent approving of the way he has handled the issue, according to a national survey by the Pew Research Center. Fifty-seven percent disapprove, even as terrorism has catapulted to the top of the public’s list of concerns.

In a news conference at the White House on Friday before leaving for a two-week vacation, Obama tried for a fourth time in 14 days to reassure a nervous nation. He urged people to stay vigilant and to refuse to be terrorized by remaining united “as one American family.”

“Squeezing ISIL’s heart at its core in Syria and Iraq will make it harder for them to pump their terror and propaganda to the rest of the world,” Obama said, using an alternative acronym for the Islamic State. He added that “our counterterrorism, intelligence, homeland security and law enforcement communities are working 24/7 to protect our homeland.”

Hours later, as Obama and his family headed to Hawaii, he made a stopover in San Bernardino, Calif., where he and the first lady, Michelle Obama, met with family members of those killed in the Dec. 2 shootings, and many of the emergency responders.

“You had people from every background, every faith; some described their loved ones who had come to this country as immigrants, others who had lived in the area all of their lives,” Obama told reporters after meeting with the families in a library at Indian Springs High School, saying their diversity was “so representative of this country.”

“As difficult as this time is for them and for the entire community,” he added, “they’re also representative of the strength and the unity and the love that exists in this community and in this country.”

In the case of the San Bernardino massacre, the president has had to calibrate his response even more carefully, sounding familiar themes about the importance of gun control but also speaking to Americans’ fears about the threat of homegrown terrorism.

“Even as we are vigilant about preventing terrorist attacks from happening, even as we insist that we can’t accept the notion of mass shootings in public places and places of work and worship, we have to remind ourselves of the overwhelming good that exists out there,” Obama said. The families, he added, “could not have been more inspiring and more proud of their loved ones or more insistent that something good comes out of this tragedy.”

Obama, in private meetings a year ago, vowed to wring every ounce of progress out of his remaining tenure and admonished his staff not to be discouraged by Republican congressional victories. His success in the past 12 months, both overseas and at home, defied expectations that gridlock in Washington and the presidential campaign would derail his plans.

But few seem to have noticed. The president’s overall job rating has hardly budged in the last year, the Pew survey found. The president’s job approval is at 46 percent even as Obama has claimed progress on economic and domestic issues, which the public now rates as less important.

“They didn’t resonate out there in any way,” William M. Daley, a former chief of staff for Obama, said of the president’s accomplishments this year.

Daley said most Americans viewed negotiating a budget deal or a transportation funding bill as a basic responsibility of government. “Yeah, we don’t have a shutdown,” he said, “but that’s like asking for credit for just doing a job.”

The president and his aides have long been frustrated by a political and media environment that they view as too focused on trivial, short-term matters. One senior White House official said Obama and his aides had reached “the acceptance phase,” recognizing that even significant accomplishments were unlikely to break through. But White House officials said the president remained focused on chipping away at his priority list in the next year.

Daley said the president had “a hard time emoting” about the terror threat because he tried to avoid the kind of bellicose rhetoric coming from the Republican presidential candidates.

But Sen. Tim Kaine, D-Va., said there was a downside to that. He said that while Obama was traveling in Asia immediately after the Paris attacks, the president and his staff missed a chance to connect with Americans on their fears about terrorism, and instead criticized lawmakers and others for focusing blame on Syrian refugees.

Carroll J. Doherty, the director of political research at Pew, said Obama’s accomplishments had failed to translate into better approval ratings in large part because they were either too obscure to grab public notice or so controversial — the Iran deal, for example — that they sparked a polarized reaction.

“Many of the accomplishments he’s touting are not very high-visibility issues, or they are very divisive,” Doherty said.

At the same time, he said, Obama has been unable to shake the perception that his response to national security threats has been weak. The share of Americans who believe the government is doing a good job reducing the threat of terrorism has fallen sharply this year, from 72 percent to 46 percent, the lowest point since the attacks of Sept. 11, 2001.

“He gets bipartisan criticism on terrorism, including among conservative and moderate Democrats,” Doherty said. “This is now Topic A for Americans, and this critique that he’s not tough enough has persisted and grown.”

At the White House, advisers say they are pleased that Obama has at least avoided lame duck status.

“He focuses on enacting policy, and he doesn’t worry about polls and the news cycle,” said Phil Schiliro, who served as the president’s chief legislative aide early in his first term. The president’s view, he added, is “that politics will sort itself out.”

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