Once the heir-apparent to long-time former premier, Mahathir Mohamad, Anwar was sacked from his post of deputy prime minister in 1998 and jailed for six years.
He became free to run for office again last week, when a five-year ban stemming from his corruption conviction expired. He now says he has the support of enough defectors to topple the government.
The Barisan Nasional coalition has ruled Malaysia for more than half a century since the former colony gained independence from the UK, but has been rocked by its unprecedented electoral setback in March.
The Pakatan Rakyat opposition alliance claimed more than a third of parliamentary seats and five states in the polls, putting Abdullah Ahmad Badawi, the prime minister, under heavy pressure.
Anwar, 60, pledged more effective governance and steps to wipe out corruption and promote racial equality.
"Our reform programme will certainly be more secure. We will push for a market economy, judicial independence and equality for all Malaysians," he said.
Anwar also repeated his claim that politicians from Sabah and Sarawak provinces had indicated interest in defecting from the ruling coalition to the opposition.
"Lawmakers in the two states in Borneo island have approached me about switching sides, but so far none has declared their intentions publicly," he said.
In eastern Sabah state, Anwar said coalition politicians could change allegiance before August after being sworn in at the end of April.
"It's all a matter of timing. Let parliament resume and they are sworn in as MPs [on April 28].... It could be the month after or by August," he said.
Anwar will travel to Sarawak on Thursday to rally support for the opposition and to press his own claims for power.
Analysts have backed Anwar's statement that he has enough support to rule, saying turmoil in the ruling coalition could hasten an exodus and propel him to power.
Abdullah is facing growing demands to quit, but has defiantly claimed a mandate to rule and refused to discuss a succession plan.
Anwar had previously been expected to re-enter parliament quickly through a by-election in one of the seats held by his Keadilan party, but says he is in no hurry to act and will instead focus on building up the opposition.