Police meanwhile have arrested two lawmakers from the Rajapaksas' Sri Lanka Podujana Peramuna in connection with last week's violence when anti-government protests turned deadly.
Sri Lanka's parliament has voted against fast-tracking an opposition move to condemn President Gotabaya Rajapaksa, as the prime minister warned that the country was down to its last day of petrol supplies.
Lawmakers voted 119 to 68 against the motion through parliament on Tuesday, which reconvened for the first time since violence flared last week and the prime minister quit.
The non-binding motion was proposed by the main opposition Tamil party, the Tamil National Alliance.
The party said the motion echoed the demands of thousands of anti-government demonstrators who have for weeks been seeking Rajapaksa's resignation.
It is likely to be debated later in the week. However, if the motion eventually passes, it could increase the pressure on the president to resign.
Police said on Tuesday they had arrested two lawmakers from the Rajapaksas' Sri Lanka Podujana Peramuna in connection with last week's violence.
More than a month of protests against the government's handling of the economy turned deadly last week when supporters of the former prime minister stormed an anti-government protest site in Colombo.
Days of subsequent clashes between protesters, government supporters and police left nine dead and more than 300 injured.
Sri Lanka's economic crisis, unparalleled since its independence in 1948, has come from the confluence of the Covid-19 pandemic, rising oil prices and populist tax cuts by the Rajapaksas.
The president's elder brother Mahinda stepped down as prime minister last week and in a bid to defuse mounting public anger, Gotabaya appointed opposition politician Ranil Wickremesinghe to replace him.
Wickremesinghe has won crucial support from the two main opposition parties to form a "unity government" to pull the country out of the dire economic crisis, but had yet to form a full cabinet on Monday afternoon.
He was expected to name a new cabinet later, but political sources said negotiations were still underway on sharing portfolios.