Bangladesh has arrested a key opposition figure and deployed thousands of police as opposition protests held to mark the first anniversary of last year's controversial polls entered a second day.

The arrest on Tuesday of Mirza Fakrul Islam Alamgir, acting secretary general of the Bangladesh Nationalist Party (BNP), came a day after four activists of the party were killed in clashes with supporters of the ruling Awami League.

Alamgir was detained as he stepped out of the National Press Club in the capital Dhaka, where he had taken shelter, police said.

"He was arrested in specific cases," police official Mashiur Rahman said, without elaborating.

The government of Prime Minister Sheikh Hasina has launched a crackdown on displays of anti-government sentiment in Dhaka as BNP leader Khaleda Zia stepped up calls for fresh elections.

Police used teargas and rubber bullets to scatter protesters in Dhaka and elsewhere.

"We had to use teargas and rubber bullets to disperse opposition activists after they smashed nearly a dozen vehicles and set off blasts," said Khayrul Fazal, a police official in the northeastern district of Sylhet.

Bangladesh authorities on Tuesday threatened to bring murder charges against Zia - confined to her Dhaka office since Saturday - over accusations that she and Alamgir incited a nationwide wave of deadly violence.

Zia, who was due to join a mass rally marking the first anniversary of the polls boycotted by her party and won by Hasina, has been barred from leaving by police.

Last January, Hasina's Awami League came to power for a second consecutive term after violent elections boycotted by 20 other smaller opposition parties, provoking criticism from international observers over the poll's legitimacy.