The UK has called for a "spirit of unity" among Kenya's political leaders to avoid further violence after an election marred by vote rigging claims.
Mr Miliband expressed concerns over alleged vote rigging
UK Foreign Secretary David Miliband said he had "real concerns" about the claims, which sparked violent protests that have left at least 10 people dead.
Kenya's President Mwai Kibaki was re-elected amid alleged irregularities.
Mr Kibaki's rival, Raila Odinga, immediately rejected the result, prompting violent clashes.
Opposition protesters began riots in Kenya's capital, Nairobi, just minutes after the election result was announced.
A team of observers from the European Union said the Electoral Commission of Kenya (ECK) had failed to ensure the credibility of the poll.
In a joint statement with International Development Secretary Douglas Alexander, Mr Miliband said the election marked a "pivotal moment for Kenya".
It was also a time when the democratic process and election outcome "has to be seen to be fair in the eyes of the Kenyan people".
The statement read: "We congratulate Kenyan voters for conducting their vote in an orderly and dignified manner. But we have real concerns at the irregularities reported by the EU observers and others.
"We call on all Kenya's political leaders and democratic institutions to work together to address those concerns, seriously, in a spirit of unity, and in a way which will bring the respect and support of the Kenyan people.
"Those leaders must also ensure the safety of Kenya's people - the tragic deaths this weekend have marred an otherwise peaceful election."
They said the violence that followed the election result must not be repeated and urged all sides to "pursue their disputes peacefully through dialogue and the appeals process".
'Healing and reconciliation'
Regarding relations between the UK and Kenya, the ministers said their country "looks forward to working with a legitimately elected government of Kenya, which commands the support of the Kenyan people".
Mr Kibaki won 4,584,721 votes, beating Mr Odinga by more than 230,000 votes, the ECK said.
Kalonzo Musyoka, another presidential contender, got 879,903 votes.
Mr Kibaki was then sworn in for his second five-year term.
In his speech, the president described the elections as "free and fair", urging all political parties to "accept the verdict of the people".
He said it was now "time for healing and reconciliation" to overcome issues dividing the nation.
Mr Kibaki also promised to form a "clean hands government" free of corruption.