Tokyo's benchmark Nikkei 225 index rises 0.2% to 19,902.58 points.
The Dow Jones also ended higher, gaining 85.33 points to settle at 20,981.94.
Investors will analyse inflation data, as well as reports on the labour market and retail sales this week.
Shares lift as Saudi Arabia and Russia agree to extend an agreement to cut oil output for a further nine months.
Major oil producers pledge to do "whatever it takes" to cut production to curb current oil glut.
Oil prices rise after Saudi Arabia and Russia say they will extend crude production cuts until March 2018.
Several Opec ministers and Russia came out in favour of extending production cuts beyond June.
US markets continue largely to ignore turmoil on the political scene.
The US president claims to be pro oil - yet his criticism of free-trade agreements dents confidence in a cross-border industry.
A weaker pound also attracted traders to the international nature of firms on the index.
Bank of England cut its growth forecast for the UK economy from 2% to 1.9% on Thursday.
Nikkei 225 share average down by 0.4% at 19,890.77 points.
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Nasdaq drops after four days of record highs.
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As US inventories decline, oil ministers of Iraq and Algeria claim there's agreement within Opec.
BoE leaves rates at 0.25% but warns inflation will peak earlier than expected.
Tokyo's Nikkei 225 benchmark index rises 0.3% to 19,959.97 points.
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Snapchat parent company stocks plummet after it reveals $2.2bn loss.
Prospect of rising US shale production continues to neuter possible price boost from Opec output cut extension.
David Brinley, oil and gas giant's General Counsel, says technology playing big part in weathering industry turbulence.
Pound closes in on $1.30 barrier for the first time in eight months ahead of Bank of England meeting.
The Hang Seng and Sensex surged by 1.08% and 0.88% respectively.
Euro falls below $1.09 for the first time since 4 May, while dollar gains ground against its main rivals.
Prime Minister Theresa May said she is 'fed up with rip-off energy prices'.
The Hang Seng registered the strongest gain of 0.47% during midday trading hours.
Gunvor co-founder and former Soviet era trade official has amassed huge wealth from the natural resources sector.
Soundbites in favour of extending oil production cuts having little impact in the face of rising US output.
'With markets rallying in expectation of Macron win, there was little upside left for equities and euro.'