Monday's poll saw Sheikh Hasina Wajed's Awami League party secure a landslide victory in an election ending two years of rule by an army-backed regime that took power after deadly clashes between rival party supporters.
The vote, the first in the country since 2001, was held amid tight security which officials said would stay in place after a ban on political activity was lifted Thursday.
"We are still suggesting that parties should be cautious," Election Commissioner Shakhawat Hossain said.
"They should not go around being very jubilant. So far so good, but there were incidents of violence that happened in the last election in 2001."
Sheikh Hasina's rival, Khaleda Zia of the Bangladesh Nationalist Party (BNP) who suffered a crushing defeat in the polls, said the result was rigged.
"Many of our party workers were forced from their position in polling booths and later beaten up," BNP spokesman Rizvi Ahmed told reporters late Wednesday, parading two men with bandaged heads he said were victims of the violence.
The BNP has been holding emergency meetings about its next move and is considering a legal challenge to the result.
Monday's election was largely peaceful with a festive atmosphere at polling booths, but police said they remained on guard for revenge attacks by losing activists and Islamic militants opposed to Sheikh Hasina.
National police chief Nur Mohammad said 600,000 officers deployed during the polls would remain on patrol.
"Security has been tightened further in places which we think are vulnerable," he said.
After independent observers, including the European Union, declared the election was free and fair, analysts say the BNP is in desperate straits.
"The party appears to have little power. It should accept the result and try to regain some strength ahead of the next election," Dhaka University politics professor Ataur Rahman said.
"But if they really do have evidence of vote rigging, they need to quickly present it."
Security for Sheikh Hasina, which was tight during campaigning amid reports that Islamic militants were plotting to kill her, would also be stepped up, the country's elite Rapid Action Battalion (RAB) security force said.
"Security to Sheikh Hasina is a top priority," RAB head Hasan Mahmud said, adding that more than 50,000 troops deployed for the election would stay in position until January 3 or 4.
As her winning margin became evident on Monday night, Sheikh Hasina called for restraint and ordered that no victory processions hit the streets.
"It feels like the city is in mourning, instead of celebrating one of the greatest victories in our political history," said Shoaib Ahmed, a Dhaka insurance agent who voted for the Awami League.
Sheikh Hasina's Awami League won Monday's election by a wide margin, taking 230 of a possible 300 seats. Zia's BNP won just 29.