"The two young men who were killed were part of the demonstrators and they started hurling stones at the officers. That is when officers fired at them," the AFP news agency reported an anonymous senior officer as saying.
Odinga said the dead included a driver for a Kenyan opposition member of parliament, who was shot by police as he attempted to leave his house in the Kasarani district.
Thursday saw the start of the second of three days of banned rallies called by Odinga to protest against Kibaki's re-election in December 27 polls.
Andrew Simmons, reporting for Al Jazeera from Nairobi, said the demonstrations were causing growing disruption despite their small size.
"Demonstrations are going on across the country. The numbers are not particularly massive, but its causing more and more destabilisation," he said.
Police fired tear gas and bullets into the air to disperse protesters in Mathare and in the western cities of Kisumu and Eldoret, witnesses said.
Paramilitary police were seen clashing with hundreds of opposition protesters, who were armed with rocks and machetes, in Mathare.
In the opposition stronghold of Kisumu, riot police fired teargas on youths who had erected roadblocks on major roads, an AFP correspondent said.
Al Jazeera's Mohammed Adow, reporting from Kisumu, said: "People have been gathering again for the second day ... they've not been gathering in large numbers but some are gathering at intersections in the town and in some of the estates they've been burning tyres and blockading some of the major roads."
The protesters had vowed to avenge the killings of several demonstrators in clashes with police in Kisumu the previous day.
Alfred Mutua, a government spokesman, blamed the violence on "gangs of organised rioters keen to loot and harass the public".
In Kisumu on Wednesday, security forces shot dead three men.
"The killings by the police is completely unjustified," Ben Rawlence of the Human Rights Watch told the Reuters news agency.
|Kenya's opposition says that the presidential |
election was rigged [AFP]
"They have not learnt their lesson since killing at least 44 people last week. They must be held accountable."
In footage shown by local broadcaster KTN, one Kisumu policeman was seen firing his assault rifle at a young man in a black T-shirt who was pulling faces at other officers.
The man in the black T-shirt fell down, then the policeman ran over and kicked him.
KTN, which said four people were feared killed in Wednesday's trouble, said the youth later died.
Across Kenya, more than 600 have been killed in riots and a wave of tribal violence since the outcome of the ballot, which international observers said fell short of democratic standards.
A quarter of a million, many of them members of Kibaki's Kikuyu ethnic group, have been forced from their homes.
The US and former colonial power Britain have called on Kibaki's government to let peaceful protests go ahead.
They and 11 other nations have threatened to cut aid if the government's commitment to "good governance, democracy, the rule of law and human rights weakens".
Since being sworn in on December 30, Kibaki, 76, has entrenched his position by naming most of a new cabinet and calling parliament to meet.
Odinga's Orange Democratic Movement (ODM) has 99 seats in the newly elected parliament, making it the largest single party but short of an overall majority.
Kibaki's Party of National Unity won 43 seats and an ally secured 16.