The "pings" were picked up during a sweep of the Indian Ocean on Tuesday by the Australian naval vessel Ocean Shield.
Angus Houston, who is leading the search operation, said sounds detected in the same area last week had been analysed and were "consistent with the specification and description of a flight data recorder".
"[The analysts] therefore assess that the transmission was not of natural origin and was likely sourced from specific electronic equipment," he said.
"I'm now optimistic that we will find the aircraft or what is left of the aircraft in the not too distant future, but we haven't found it yet because this is a very challenging business."
Despite the two new detections, Houston acknowledged that search crews were running out of time in the hunt for the Malaysia Airlines aircraft's two black boxes, as batteries powering transmissions run down.
Signals picked up at the weekend were held for more than two hours, while the latest sounds lasted for just five-and-a-half minutes and seven minutes.
Once the beacons fall silent, locating the flight recorders, thought to be in water some 4.5 kilometres deep, would be an immensely difficult, if not impossible, task.
"We need to, as we say in Australia, 'make hay while the sun shines'," Houston said. "I believe we are searching in the right area but we need to visually identify the aircraft before we can confirm with certainty that this is the final resting place of MH370."
No other ships are allowed near the Ocean Shield while it pulls along the "towed pinger locator" because its work must be done in an environment as free of noise as possible.
A modified Royal Australian Air Force AP-3C Orion has been parachuting sonar buoys into the vicinity. The buoys float on the surface and have a hydrophone dangling 300 metres below to hopefully pick up any transmissions. Officials warned though that transmissions could be dulled by thick silt on the seabed.
Houston said a decision had not yet been made on how long searchers would wait before an unmanned submarine was deployed. Such a vehicle will use sonar to map the seabed, a long, laborious task.
The search for debris on the surface of the ocean picked up intensity yesterday, with 15 planes and 14 ships scouring an area of 75,427 square kilometres northwest of Perth. Flight MH370 and the 239 people it was carrying vanished on March 8 after leaving Kuala Lumpur for Beijing.
Watch: Australian ship detects new signals as plane hunt narrows
Associated Press, Agence France-Presse