Secretary of State John F. Kerry said Wednesday that the United States will open its doors to more refugees over the next year but would not say how many might be Syrians fleeing war and chaos.

“We are committed to increasing the number of refugees that we take,” Kerry said after meeting with the immigration subcommittee of the Senate Judiciary Committee. “And we are looking hard at a number that we can specifically manage. . . . That’s being vetted fully right now, and I think at the appropriate time we’ll have a better sense of what exactly that number will be.”

The flood of people seeking asylum in Europe is prompting calls for the United States to admit many thousands more Syrians.

In recent weeks, desperate Syrians have crawled across barbed wire and headed by foot to Germany seeking asylum. They are the vanguard. Hundreds of thousands and perhaps millions more migrants are expected to follow.

Some lawmakers are saying the United States is not shouldering its share of the burden.

Fewer than 1,600 Syrian refugees have been admitted since 2011, the vast majority arriving just this year. Another 300 or so are expected by year’s end. But that is a small fraction of the more than 18,000 names the United Nations High Commissioner for Refugees says it has submitted for consideration, a number growing far faster than it is being whittled down.

The International Rescue Committee has called on Washington to admit 65,000 Syrian refugees by 2016. In May, 14 Democratic senators sent a letter to President Obama urging the same.

“It is not too late to do the right thing,” said Sen. Patrick J. Leahy (D-Vt.) in a statement Wednesday after meeting with Kerry.

Noting that Pope Francis has asked Europeans to shelter refugees from war and hunger, Leahy added, “In the United States, we can do the same thing. We can respond, as we have before, with meaningful action that is worthy of a nation of immigrants with by far the largest capacity to act, as the world expects us to.”

The United States has taken in 70,000 refugees from around the world in each of the past three years, more than all other countries combined.

But when it comes to Syrians, the United States has lagged far behind several European countries lately. That’s largely due to the time-consuming screening procedure to block Islamist militants and criminals from entering the United States under the guise of being legitimate refugees.

As a result, it takes 18 to 24 months for the average Syrian refu­gee to be investigated and granted refu­gee status. The process takes so long that the UNHCR takes biometric images of some applicants’ irises to ensure that when refu­gee status is eventually granted, it goes to the same person who applied.

A record number of migrants and refugees are attempting perilous journeys to find a safer, better life in Europe. Here's why they're leaving and how they're being received. (Jason Aldag and Gillian Brockell/The Washington Post)

“We’re trying to weed out people who are liars, who are criminals or would-be terrorists,” said a senior State Department official, speaking on the condition of anonymity about administration discussions on the refu­gee crisis. “This is something that slows down the process, and it’s taken seriously by everyone involved.”

The official said the United States had been planning to introduce a “modest” increase in the number of refugees admitted — not only Syrians but refugees from Congo, where human rights abuses are rising.

The administration has spent $4.1 billion on humanitarian aid since the Syrian conflict began. Some of that money has gone to help feed and shelter the refugees, and some has aimed to help neighboring countries such as Lebanon, Turkey and Jordan cope with the burden of so many refugees.

The goal is to keep refugees in the region instead of fleeing to Europe and beyond, a prospect that appears more unlikely with every passing day.

In Congress, some lawmakers oppose raising the quota to accommodate more Syrian refu­gees, fearing national security could be compromised if they are admitted without adequate scrutiny.

In 2009, two Iraqis linked to al-Qaeda were discovered living as war refugees in Bowling Green, Ky.

The concern about refugees from Syria is particularly acute because it is the base of the Islamic State, where militants have declared a caliphate and urged their supporters to strike against the West.

Although Kerry has said that U.S. security agents are “super vetting” refugees from Syria, Rep. Michael McCaul (R-Tex.), chairman of the Homeland Security Committee, worries that terrorists will use the refu­gee crisis to slip into the United States.

“Terrorists have exploited the refugee process to sneak into our country in the past, and officials have warned my committee that we lack the on-the-ground intelligence in Syria needed to confidently vet individuals for resettlement,” McCaul said. “Before taking on any new refugee admissions, the president must provide assurances to Congress and the American people that our security screening is up to the task.”

Jon B. Alterman, who directs the Middle East program at the Center for Strategic and International Studies, said that the push to accept more refugees into the United States is complicated by “a serious intelligence problem” posed by applicants from Syria, where the hurdles of gathering background information are often insurmountable.

“How do you vet people when you don’t have a cooperative government to help you vet them?” he asked. “That, from a homeland security perspective, is a huge obstacle.”

Sen. Timothy M. Kaine (D-Va.) called for creating a safe zone in Syria so refugees can stay.

“Why not create that safe zone in Syria so people don’t have to leave their country,” he said. “They would rather stay there if we can guarantee safety and basic comforts of food, shelter and medical care. . . . If we can create that, then people will come back.”

Others acknowledged that the solutions would not be simple.

“It’s a disaster, and we’ve got to figure out a way to play an appropriate role,” said Sen. Bob Corker (R-Tenn.). “I want to address it more fully than just saying yes or no, but we certainly have a role to play.”

Sen. Amy Klobuchar (D-Minn.), who co-wrote the letter urging the administration to accept more Syrians, said screening should be stepped up so more refugees could be admitted quicker.

“I want to continue strong screening,” she said. “But there needs be a more major focus on getting screening done. I’m not calling for an end to it. I’m calling for making it a priority.”

Although refugees have been coming to the United States throughout its history, the high point was in the Vietnam years of the early 1970s, when 150,000 to 200,000 refugees were admitted every year. But admissions ground to a halt after the terrorist attacks of Sept. 11, 2001, and later resumed at a diminished level.

Juliet Eilperin and Karoun Demirjian contributed to this report.