On Monday, he met held talks with Ichiro Ozawa, the DPJ secretary-general, who is often described as the party kingmaker.
Hatoyama, who was expected to meet Ozawa again later on Tuesday, signalled that he wanted to stay on in his post, telling reporters that he wanted to "cooperate with him [Ozawa] to tackle national challenges."
|The US base on Okinawa has been a contentious issue for several years [Reuters]
Local media, quoting party sources, also said the two would discuss whether Hatoyama should resign ahead of the election for the upper house of parliament on July 11.
The decision over the Futenma base has angered tens of thousand of residents on Okinawa who have complained about noise levels, pollution and crime associated with the base, and want the base moved off the island entirely.
Hatoyama took office last September pledging to create a "more equal" relationship with the US.
He had promised to move the marine base off the island, which hosts more than half the 47,000 US troops stationed in Japan under a 50-year-old joint security pact.
However, US military officials have argued it was essential that the base remain on Okinawa because its helicopters and air assets support marine infantry units based there.
Moving the facility off the island, they said, could slow the marines' coordination and response in times of emergency.