PRAGUE (Reuters) - A junior partner in the Czech Republic's shaky coalition signaled on Thursday it may back off its threat to leave the cabinet, reducing the chances Prime Minister Petr Necas will fall.

The turnaround, still subject to further negotiations, would resolve the latest in a series of crises that have hurt the government's ability to push through legislation and brought frequent policy changes.

The small centrist LIDEM party's ministers handed in resignations in December after Necas fired the party's boss, Karolina Peake, as defense minister just eight days after she took office and fired several senior ministry officials.

But Peake said on Thursday that she would advise the party, whose popularity is close to zero in opinion polls, to stay in the center-right coalition and thus keep it afloat.

"I will be recommending staying in the government, but only on the condition that some of our demands are met," Peake told Czech Television, referring to setting up an oversight body for party financing and creating a law to define the duties and rights of people working in state administration.

Necas's three-party coalition started its four-year term in 2010 with a strong majority, raising hopes of sweeping economic reforms. But the majority disappeared in a series of coalition rifts as the Czech economy has sagged.

The government has raised taxes and cut welfare to slash the budget deficit that swelled in 2009 when the global economic crisis hit the export-dependent economy. After renewed recession last year, the government expects the economy to grow 0.7 percent in 2013.

Peake's party leadership was due to meet later on Thursday to discuss its future support for the cabinet.

(Reporting by Jan Lopatka; Editing by Ruth Pitchford)