At a closed Senate session, Senators of the People's Democratic Party (PDP) tried to introduce a motion giving Buhari six-weeks to improve the country's security or face impeachment, Senator Philip Aduda said on Wednesday.
"Nowhere is safe in Nigeria, even Abuja. Urgent steps need to be taken...we have given the president six weeks to resolve the issue or we impeach him," he said.
Aduda said the motion was blocked by the Senate President, prompting a walkout by opposition Senators. Parliament is controlled by the ruling All Progressive Congress (APC) party and any move to impeach Buhari would require support by two thirds of Senators.
The presidency in a statement backed the Senate President for not "entertaining the ridiculous motion to impeach our President".
Nigeria is struggling with security problems across its vast territory, including armed robberies by criminal gangs, an Islamic insurgency in the northeast and a spate of mass school abductions in the northwest.
The government's information minister Lai Mohammed said the impeachment move was propaganda.
"We are working round the clock...to make sure the situation is brought under control," Mohammed said.
Nigerian authorities ordered schools in the capital Abuja to close on Wednesday two days ahead of summer holidays to avoid them becoming soft targets for terror as insecurity spreads, highlighting the country's security challenges.
Nigerians go to the polls in February 2023 to elect a new president in a hotly contested vote where security and the state of economy will be the main issues.