Ministers are also expected to agree this week a doubling in funding for aviation security.
It comes after Friday`s deadly attacks in Paris that left 129 people dead, including one Briton. So-called Islamic State claimed responsibility.
Prime Minister David Cameron said: "This is a generational struggle that demands we provide more manpower to combat those who would destroy us and our values"
A one-minute silence for the victims of the Paris attacks will be held in the UK at 11:00 GMT. It will be part of a Europe-wide silence at midday French time.
Briton Nick Alexander from Essex has been confirmed dead and Home Secretary Theresa May said other Britons had been injured.
""Manhunt for Paris attacks suspects
The funding for the 15% increase in staffing for the three intelligence agencies has been revealed ahead of the publication of the government`s Strategic Defence and Security Review, which is expected next week.
BBC home affairs correspondent Daniel Sandford said this was an increase on the number previously briefed to the media by the Treasury.
The intelligence agencies already have about 12,700 staff.
Putin meeting
The extra funding for aviation security is expected to be used to pay for more experts to assess airport safety in countries with large numbers of British visitors, among other measures. The UK currently spends about £9m a year on this issue.
Mr Cameron is set to meet Russian President Vladimir Putin later in their first face-to-face talks for a year at the G20 summit in Turkey.
He is expected to urge Mr Putin to co-operate with the US-led coalition in the fight against Islamic State militants and their talks will also focus on new efforts to end the civil war in Syria.
Meanwhile, officers from the Metropolitan Police`s Counter Terrorism Command unit are interviewing people returning to the UK from France who may have information about the Paris attacks.
The Met is also appealing for any potential witnesses to contact its anti-terrorist hotline, on 0800 789 321.
""Mr Alexander, 36, from Colchester, died in the attack at the Bataclan concert hall, where he had been selling merchandise.
His family described him as "generous, funny and fiercely loyal".
Friends also paid tribute to him on social media. Joe Trohman, lead guitarist of the rock band Fall Out Boy, described him as a "great guy".
More than 80 people died at that concert hall, one of a number of locations targeted by attackers.
The US band Eagles of Death Metal were playing a gig when militants burst into the venue and opened fire, but the band themselves survived unscathed.
Other bands, including U2, Motorhead and Foo Fighters, have cancelled gigs in Paris.
