"The youth are calling for a change in the existing system," Wickremesinghe said, laying out plans for 15 committees that would work with parliament to decide national policies.
"I propose to appoint four youth representatives to each of the 15 committees," he said, adding that they could be drawn from the current protesters.
The demonstrations led to tense scenes in Colombo, where authorities struggled to disperse large crowds and chemical irritants hung over the streets.
Several men were seen picking up canisters spewing tear gas and throwing them back towards the police who fired them.
Female medical and science students joined the protests, with many running for cover when authorities unleashed water cannon.
Wickremesinghe is not from Rajapaksa's party, but was given the job after the president's elder brother Mahinda resigned as prime minister on 9 May following weeks of protests, and when no other legislator agreed to step in.
Wickremesinghe is the sole parliamentary representative of the United National Party, a once-powerful political force that was nearly wiped out in Sri Lanka's last elections.
Rajapaksa's party, which has a majority in the legislature, has offered to provide him with the necessary support to run a government.
Sunday's student action came a day after a similar clash when protesters tried to storm Rajapaksa's heavily guarded colonial-era official residence, where he has bunkered down since thousands surrounded his private home on 31 March.
An unprecedented shortage of foreign exchange to import even the most essential supplies, including food, fuel and medicines, has led to severe hardships for the country's 22 million people.
The government last month asked the International Monetary Fund for urgent financial assistance. Talks are continuing.
The country has defaulted on its $51 billion foreign debt.
Its currency has depreciated by 44.2 per cent against the US dollar this year, while inflation hit a record 33.8 per cent last month.