He made the call at a rally in Jaffna, making a final push for votes in the country’s former warzone.
While he remains popular among ethnic majority Sinhalese voters, Mr Rajapakse is widely detested by members of the country’s biggest minority, after he oversaw the brutal crushing of a 37-year-long Tamil rebellion.
The main Tamil party has already endorsed the president’s chief rival, Maithripala Sirisena, in the January 8 election.
However, the incumbent told voters in the northern Jaffna region that he was committed to improving their livelihoods, pointing to improvements in infrastructure.
“This is my 11th visit to Jaffna as president,” said Mr Rajapakse, who has been in power for nearly a decade, making him the longest-serving leader in South Asia.
“The devil you know is better than the unknown angel,” he said in Sinhala, speaking through a translator.
“I am the known devil, so please vote for me.”
He then listed a series of infrastructure projects that had been completed since the end of the Tamil separatist conflict in 2009.
“We gave you electricity, we gave you new schools and now we want to give you proper water supplies,” he said, in a region which was devastated by the separatist conflict.
The president had been due to inaugurate the latest stretch of a reopened rail link from the capital Colombo to Jaffna, but he cancelled his plans at the last minute, leaving his transport minister to do the honours.
Tamils account for around 13 per cent of the 15 million people entitled to cast their ballots next Thursday and their choice of candidate could be crucial to the outcome of what is shaping up to be a tight contest.
Mr Rajapakse had been the clear favourite but a series of defections by allies, including his one-time health minister Mr Sirisena, have thrown the contest wide open and the president now needs every vote he can muster.
Although the economy has been growing at rates of around seven per cent in the post-war era, many voters say that ruling party cronies have been the only ones to really benefit.
Earlier, the opposition’s Ranil Wickremesinghe claimed the government had sent troops to the north and east, to keep Tamil voters away from the polls.
He said the opposition would publish the names of military officers assigned to disrupt the vote and warned them to back off.
Mr Rajapakse called the snap election two years ahead of schedule after his party’s popularity dropped 21 points at a local election in September.
However, his ruling coalition has faced several blows, including the withdrawal of support from the country’s main Muslim party and, more recently, the defection of his former deputy investment minister, Faizer Mustapha.
The Brussels-based International Crisis Group said in a report last month that he may resort to the use of the military to remain in power.
Government warns against EU intervention
Meanwhile, Sri Lanka warned the European Union not to be “prescriptive” about next week’s presidential elections, after ambassadors in Colombo urged the government to ensure a peaceful election.
The Ministry of External affairs took objection to a statement issued earlier on Friday by European ambassadors that Sri Lankans should be “free to choose their leaders without violence or fear”.
“Domestic elections are not for foreign government representatives to be prescriptive about, that too, a few days ahead of the polls,” the ministry said in a terse statement.
It accused the diplomats of commenting “on an issue of a strictly domestic nature” and added that Sri Lanka was capable of holding free and fair elections. (AFP)