A UK ship with sophisticated detection equipment, HMS Echo, has arrived in an area where a Chinese vessel searching for the missing Malaysian plane has twice detected a pulse signal.
Australian ship Ocean Shield is first investigating a possible third signal elsewhere in the massive search zone.
None has been confirmed as coming from the flight recorders of MH370.
Meanwhile families of the missing passengers have attended a prayer service in Kuala Lumpur.
The plane disappeared four weeks ago with 239 people on board.
Investigators believe it crashed in the Indian Ocean although no confirmed debris has been found.
Australian co-ordinators said on Sunday that new analysis of satellite data meant efforts would now focus on the southern part of the search zone, near where China's vessel is located.
Air Chief Marshal Angus Houston said China's Haixan 01 had redetected a signal for about 90 seconds on Saturday, within hours of it being heard earlier.
He said the latest discovery was about 2km (1.2 miles) away from the original pulse, and that China had also reported spotting white objects on the surface of the water about 90km away.
"The fact that we have two detections - two acoustic events - in that location provides some promise," he said.
However he said these signals were "fleeting encounters" that could not be verified until the arrival of British naval ship HMS Echo and Australian defence vessel Ocean Shield.
Both vessels have technology able to detect underwater signals emitted by "black box" data recorders.
HMS Echo arrived around 15:45 GMT on Sunday. The depth of the water in this zone is said to be about 4.5km (2.8 miles).
Ocean Shield - described by officials as the best equipped vessel taking part in the search - will head there once it has investigated a third acoustic detection about 300 nautical miles away (560km).
It is not expected to reach the southern area for over a day.
As crews began day 30 of the search on Sunday, Air Chief Marshal Houston told reporters investigators were "running out of time" in the search for the flight's "black box".
The battery-powered signal from recorder can begin to fade after 30 days.
Thousands of people, including families of the missing passengers, attended the prayer service in the Malaysian capital on Sunday.
"This is not a prayer for the dead because we have not found bodies. This is a prayer for blessings and that the plane will be found," said Liow Tiong Lai, the president of the Malaysian Chinese Association (MCA), one of the parties in the governing coalition.
A dozen military aircraft and 13 ships are searching three areas about 2,000 km (1,240 miles) north-west of the Australian city of Perth.
The areas cover a total of 216,000 sq km (560,000 square km).
Haixun 01 picked up the first so-called "ping" signal at about 25 degrees south latitude and 101 degrees east longitude, state-run Xinhua news agency said.
The signal reportedly had a frequency of 37.5kHz - the same as that emitted by the flight recorders.
Three people on board the boat were said to have heard the pings, which were not recorded as they came suddenly.
Flight MH370 disappeared en route from Kuala Lumpur to Beijing on 8 March.
Malaysia earlier announced it had set up three ministerial committees to help co-ordinate the search, and a new investigation team which would include members from Australia, China, the US, the UK and France.