The proposal follows calls from lawmakers and human rights groups for Mr. Obama to expand the number of Syrian refugees accepted into the U.S. beyond the nearly 1,600 that have been allowed into the country since 2011.

The migrant crisis, the worst since World War II, is adding urgency to stymied efforts to address the Syrian civil war, U.S. officials said, and has given a boost to an emerging shift in the international fight against Islamic State militants, as the U.S.-led military coalition begins to focus more heavily on Syria.

“Everything is interwoven,” a senior administration official said Thursday.

The 10,000 Syrians allowed into the U.S. over the next year would be in addition to those here now, administration officials said.

White House press secretary Josh Earnest cast the decision as a “significant ramping up” of the U.S. response to the crisis. He said Mr. Obama personally directed aides to “make preparations to accept at least 10,000 Syrian refugees in the next fiscal year,” which starts in October.

Some human rights advocates said the president’s response doesn’t go far enough.

“This is not leadership, it is barely a token contribution given the size and scale of the global emergency,” said Eleanor Acer, director of the refugee protection program for U.S.-based Human Rights First.

Rights advocates have called on the administration to accept as many as 100,000 Syrians.

More than 4 million Syrians have fled the country since the civil war began in 2011.

American allies in recent weeks expanded their efforts to accommodate more refugees. Germany indicated it could take as many as 800,000, and the U.K. plans to accept 20,000 over next five years. Australia announced Wednesday it would accept an additional 12,000 refugees from both Iraq and Syria. Canada has resettled about 2,500 Syrians so far and plans to accommodate 11,300 refugees by 2017.

The U.S. is the largest bilateral contributor to humanitarian relief efforts in Syria, having given more than $4 billion since 2011. But the administration has admitted only about 1,200 Syrian refugees this year. In fiscal year 2014 the U.S. admitted about 100 Syrian refugees.

Mr. Obama’s proposal would require approval from Congress, which is debating spending issues in coming weeks. Republican and Democratic lawmakers have called for Mr. Obama to more aggressively address the crisis, but are divided on how.

Some worry that accepting migrants from countries where extremist groups are active could put the U.S. at risk.

Intelligence and law enforcement officials have said they fear Islamic State militants could embed with groups of refugees and eventually make their way into the U.S.

“We have to make sure we understand who is coming in to the best of our ability because there is a risk there,” Federal Bureau of Investigation Director James Comey said.

Mr. Earnest, the White House press secretary, said the administration would not relax any of the procedures for vetting refugees before they can enter the country. For Syrians, that process can take 18 to 24 months, given the potential security threats, U.S. officials have said.

“The president will not sign off on a process that cuts corners,” Mr. Earnest said.

Rep. Michael McCaul (R., Texas), chairman of the House Homeland Security Committee, criticized Mr. Obama’s proposal to accept more Syrian refugees, saying the migrant crisis should instead be addressed in Syria.

“It is heart-wrenching to watch innocent Syrians fleeing the violence in their country, and we can do more to help. But the best way to solve this crisis is at the source,” Mr. McCaul said.

Other Republicans said the U.S. shouldn’t take the lead on admitting refugees, citing security and cost concerns.

“Middle Eastern nations should assume the primary task of absorbing this wave of refugees,” said Sen. Jeff Sessions (R., Ala.), a member of the Senate Judiciary Committee.

Still other lawmakers said Mr. Obama’s proposal fell short.

“We’d like to see more, but it is still a positive step,” said Sen. Amy Klobuchar (D., Minn.), one of 14 senators who called on Mr. Obama in May to resettle thousands more refugees. “Refugee resettlement had not been a major focus and that’s why a number of us had been pushing it because we knew the numbers were small compared to the need. Very small.”

U.S. officials, concluding that the only long-term resolution to the migrant crisis is stabilization in Syria, are reviewing the current approach to both the civil war and the fight against Islamic State.

“What really needs to happen here is Syria returning to being a place where people don’t have to flee the violence, the persecution and the war,” State Department spokesman John Kirby said Thursday.

In recent weeks, France and Australia have committed to airstrikes against Islamic State militants in Syria, and British Prime Minister David Cameron said he would seek legislative approval to expand the U.K.’s military involvement beyond Iraq and into Syria.

The U.S. and Turkey, meanwhile, are focusing on Islamic State-held areas along the Syria-Turkish border.

The administration also is looking for ways to advance troubled diplomatic efforts to end the Syrian civil war, but U.S. officials are newly concerned that Russia, a key partner in diplomatic efforts, is stepping up its support to the regime of President Bashar al-Assad.