As the search for a missing AirAsia passenger plane stretched into its third day, authorities widened their hunt and asked for outside help, even as hopes dimmed among families of the 162 people aboard the jet.

Indonesian authorities said Monday that they believe the plane already lies at the bottom of the sea, complicating the search and prompting them to ask the United States, Britain and France for more advanced equipment.

The Pentagon said that details of that assistance are being worked out but that it would probably include “air, surface and sub-surface detection capabilities.”

An Indonesian helicopter crew Monday afternoon spotted two oily patches. But search officials said it was too soon to tell whether they were related to the Singapore-bound aircraft, whose last contact with air-traffic controllers Sunday was a request by the pilot to climb to 38,000 feet after encountering rough weather. Bambang Soelistyo, chief of the National Search and Rescue Agency, told reporters Monday that authorities believe the main wreckage has already sunk to the seabed, based on the plane’s last coordinates and its estimated crash position, near Belitung island in the Java Sea.

In a statement issued late Monday, search officials said they have deployed 12 helicopters, 11 planes and 32 ships, including assets from Malaysia, Singapore and Australia, with more than 1,100 personnel involved. Even fishing boats have been tapped in the widespread search for the wreckage, authorities said.

The U.S. Navy said the USS Sampson, a guided-missile destroyer that is already in the region, would join the search later Tuesday.

The father of the pilot, Iriyanto, who like many Indonesians only has one name, told reporters he was making peace with God over his son’s likely death. “I want my son to come back alive and well, but if that’s not meant to be, if God doesn’t want that, it’s in the hands of fate,” Suwarto told the BBC.

And the sister of the French co-pilot, Remi Plesel, told a radio station, “We want them to find the plane, to explain to us what happened.” But Renee Plesel said she realized that “when a plane falls out of the sky, there are hardly any survivors.”

The sudden disappearance and frustrating maritime search are eerily similar to those in the case of Malaysia Airlines Flight 370, which disappeared over the Indian Ocean in March. The whereabouts of the plane, with 239 people aboard, are still a mystery.

Indonesia’s state-owned navigation provider, AirNav, gave local media a detailed account Monday of Flight 8501’s last contact with air-traffic controllers Sunday.

Wisnu Darjono, AirNav’s safety director, said the pilot asked Soekarno-Hatta Airport’s air-traffic control at 6:12 a.m. for permission to turn left to avoid bad weather. Permission was granted, and the plane turned seven miles to its left flank, the Jakarta Post reported.

The pilot then asked to climb from 32,000 to 38,000 feet but did not explain why.

Jakarta’s air-traffic control conferred with Singapore-based counterparts and agreed to allow the plane to increase its altitude to 34,000 feet because a second ­AirAsia flight, 8502, was flying at 38,000 feet. But by the time air-traffic controllers relayed the permission to climb at 6:14 a.m., there was no reply, Darjono said.

Investigators are trying to locate debris from the crash and then work backward, following currents, to find the wreckage on the seabed. To do so, they will need ships equipped with advanced sonar and search vehicles that can look for signs of the wreckage underwater, experts said.

Once the wreckage is found, the cockpit voice and flight data recorders will offer the most substantial clues as to what went wrong.

After two days of challenging search conditions, authorities can expect “perfect weather” Tuesday and Wednesday, Adi Eka Sakya, the head of Indonesia’s Meteorology, Climatology and Geophysics Agency, said at a Jakarta news conference.But torrential rains could return Friday.

An Australian search plane Monday reported seeing objects hundreds of miles away, but Indonesian officials later said they were unrelated to the plane.

Even as the reason for the crash remained unclear, shares of AirAsia dropped sharply in trading Monday.

Indonesian officials’ speculation that the plane is already underwater would explain the lack of a signal from its emergency locator transmitter, said Australia-based aviation security expert Desmond Ross.

“All these aircraft have this beacon that triggers on impact and sends a signal to satellites,” Ross said. “If it’s gone to the bottom of the sea, we probably wouldn’t hear that signal.”

Experts said the plane’s disappearance has raised several tantalizing questions.

Bad weather appeared to play a role, but it is unclear why the pilot was not able to avoid it earlier, Ross said, noting that modern commercial jets are equipped with radar that can spot bad weather more than 100 miles ahead.

The speed of the airplane is likely to be at the forefront of any investigation, said John Cox, a former accident investigator. Radar suggests that the plane was flying at a low speed, Cox said. Overly slow speed at a high altitude could cause an airplane to stall, with insufficient lift to sustain flight, he said.

Geoffrey Thomas, editor of AirlineRatings.com, said he reviewed radar data of the flight obtained by other A320 pilots showing the plane at an altitude of 36,300 feet and climbing and traveling at 353 knots, or roughly 406 miles per hour — relatively slow for that altitude.

Many experts have compared the AirAsia flight to the crash of an Air France airliner in 2009 in which airspeed measurements failed, leading pilots to put the plane into a stall. While wreckage of the Air France flight was spotted within days, it took two years for the black-box recorder to be found and retrieved from the Atlantic Ocean.

“But I don’t think it will take nearly as long in this case,” Cox said, noting that the waters now being searched are much shallower and the search area smaller.

Brian Murphy in Washington and Gu Jinglu and Liu Liu in Beijing contributed to this report.