Hundreds of American citizens trapped in Yemen’s roiling violence have a legal right to be evacuated by the U.S. government, advocacy groups argued in a lawsuit filed Thursday that challenges the State and Defense departments' perceived inaction on a constitutional basis.

In court documents that name Secretary of State John Kerry and Defense Secretary Ashton Carter as defendants, U.S.-based lawyers acting on behalf of 41 American citizens or permanent U.S. residents stuck in Yemen described Washington's decision not to provide any flights or ships out of the conflict zone as "arbitrary" and even illegal. The plaintiffs say they are in grave danger from the escalating violence but have received little more from the State Department than emails or calls about possible third-party flights out of the country and recommendations that they take shelter.

Abed Ayoub, the national legal policy director at the American-Arab Anti-Discrimination Committee (ADC), said his group and two others that formed the Stuck in Yemen legal action group decided to file a suit as a last-ditch effort to compel the U.S. to act.

“You have infants of just a few months all the way up to the elderly, all facing bombing, guns and threats of imminent death,” Ayoub said. “They don’t have time to wait for State Department bureaucracy anymore.”

Ever since the U.S. Embassy in Yemen was closed in February — a decision made as Houthi rebels seized the capital, Sanaa, and the country teetered on the brink of civil war — Americans living in the country have felt stranded, “with nowhere to turn for logistical support and assistance needed to evacuate,” the lawsuit says. The danger in Yemen has escalated sharply in recent weeks after a Saudi-led coalition backed by the United States began to bomb the Houthis. Hundreds of fighters and civilians have been killed, including at least one American.

While other countries have scrambled to evacuate their nationals in Yemen by the thousands, the State Department has limited its efforts to sending alerts about flights coordinated by the Indian government or the International Organization for Migration (IOM) that Americans are eligible to board. In addition to India, at least six countries — China, Russia, Pakistan, Somalia, Jordan and Turkey — have all secured their citizens safe passage out of Yemen.

“It’s difficult to understand how the world’s largest military is unable to do this when much smaller countries with much less stable governments have been able to evacuate thousands,” said Zahra Billoo, an attorney for the Council on American-Islamic Relations (CAIR), which is part of the Stuck in Yemen coalition.

Those stranded say that even when the State Department alerts them to evacuation options, the phone numbers provided are frequently unreachable. Others report that transportation options recommended by the U.S. Embassy entail hefty bribes to middlemen or fees of up to $700. One frustrated relative told Al Jazeera that a U.S. official advised her relative in Yemen to find a commercial flight from the airport in Sanaa — which is now closed and subject to sporadic bombing.

Amber Eltaieb of New York City told Al Jazeera that she has spent much of the last week calling the State Department, U.S. embassies in the region and various IOM offices in an effort to get her sister, also a New York City native, out of Yemen. The problem, Eltaieb said, is that her sister’s Syrian husband, who owns a dairy store in Sanaa, is not yet an American citizen, since the two have been married only four months. He was turned away from a recent IOM flight because he lacked proper travel documentation, which Eltaieb and her sister have been unable to get from the State Department despite repeated attempts.

“The only solution they’re offering is for my sister to completely abandon her husband,” Eltaieb said.

A State Department official declined to a comment on the lawsuit to Al Jazeera. The official did not offer an explanation for why the U.S. government has made no plans to provide transportation out of Yemen for its citizens, even as it supports Saudi-led airstrikes.

Privately, however, U.S. officials have expressed concerns to Stuck in Yemen lawyers that gathering hundreds or thousands of Americans in one place to be evacuated would be unsafe because they would be an easy target for attack. The lawyers don't find that explanation convincing. In 2006, they noted, more than 15,000 Americans were safely evacuated from Lebanon after war suddenly broke out between Israel and the Lebanese faction Hezbollah.

“The talking point they’re giving us is that it would be too dangerous, but we’re not buying that,” said Ayoub.

Stuck in Yemen has registered over 400 Americans in the country through a form on its website. The figure is probably far higher, its lawyers said, perhaps even in the thousands, though the State Department does not release its estimates, for safety reasons.

With few viable options for escape and the window for evacuation closing — the IOM, for one, has said it may offer flights only for another week — some Americans have begun to explore unorthodox methods.

California native Mokhtar Alkhanshali spent several days trying to get concrete answers from U.S. embassies in the region, to no avail. Feeling abandoned by his government, Alkhanshali, who runs a business in Yemen, Mocha Mill, that helps coffee farmers sell their products abroad, hired a powerboat to take him across the Red Sea from the port city of Mokha.

The six-hour ride took him to East Africa, where he managed to secure a flight through Amsterdam back to his home in San Francisco, three days later. “It was very stupid what I did,” he told Al Jazeera. “But I realized I had to take matters into my own hands. I had to take extreme risks.”