Ugandan police have fired tear gas at supporters of opposition leader Kizza Besigye, hours after the country's president was sworn in for a fourth term in office.

Thousands of people had taken to the streets of the capital, Kampala, to welcome Besigye, the country's leading opposition politician, back to Uganda from Kenya on Thursday.

But the crowd began to flee as police used water cannons to scatter them. 

"The crowd was dispersed by police and soldiers. They fired tear gas and water cannons and chased people away with sticks," Al Jazeera's Malcolm Webb, reporting from Kampala, said.

Soon after, however, Besigye's supporters regrouped and continued to march toward the capital.

The outpouring of support for Besigye took place as president Yoweri Museveni was being sworn in for a fourth term after 25 years in power.

Already in Kampala, leaders of Nigeria, Ethiopia, Kenya, Zimbabwe, Tanzania, Democratic Republic of Congo, Somalia and South Sudan were all present for Museveni's inauguration.

But violence broke out after the ceremony, as police opened fire after a crowd attacked a car carrying Nigeria's president Goodluck Jonathan as his convoy headed to the airport to leave Uganda.

"As they came past, protesters threw stones [and] smashed some of the windows," Al Jazeera's Webb reported. "When police moved in to disperse those protesters, somebody was shot."

Elections challenged

Thursday's ceremony marked Museveni's fourth swearing in as Uganda's president, after promising in 2001 to retire from politics.

According to official results from last February's election, Besigye, 55, won 26 per cent of the vote, while Museveni, 62, took 68 per cent.

But Besigye's Forum for Democratic Change (FDC) says the results were falsified, and that both candidates received just under 50 per cent of the vote, an outcome that would have required a run-off.

Museveni has accused the opposition of trying to spread chaos in response to its loss in the election, saying on Tuesday that he planned to introduce constitutional amendments that would see bail prohibited for
certain charges, including rioting and economic sabotage.

Besigye and other opposition politicians have been released on bail after recent protest-related arrests.

The opposition figure had been in Kenya seeking treatment for injuries he suffered in a series of demonstrations against rising food and fuel prices. The demonstrations left at least five people dead.

Besigye was first taken to hospital in Kampala at the end of April after Ugandan police smashed the windows of his car and sprayed him with tear gas in an incident caught on camera. He was then transferred to a Nairobi hospital.

He told Al Jazeera at the time that he remained committed to non-violent protest.