Roger Federer kept alive his hopes of a seventh ATP Finals crown on Tuesday, beating Italian debutant Matteo Berrettini 7-6 (7/2), 6-3 at London's O2 Arena.

The Swiss third seed put himself under enormous pressure by losing his first match on Sunday in straight sets in Group Bjorn Borg to Dominic Thiem.

The six-time champion was not at his fluent best on Tuesday but ultimately had too much for Berrettini, who won just three games against Novak Djokovic in his opener.

Both players were solid on serve in the first set, with Federer struggling to make inroads against the eighth seed.

The Swiss eventually earned himself the sniff of a chance in the 12th game, winning the first break point of the match but Berrettini snuffed out the danger and held to take it into a tie-break.

Federer upped the level of his game in the shootout, helped by some wayward shots from his opponent plus a Berrettini double-fault and won it comfortably 7-2.

The Swiss, clad in black, broke immediately at the start of the second set to leave the Italian with a mountain to climb.

Berrettini earned a clutch of break points in the eighth game but Federer eventually served himself out of trouble.

Federer, as usual enjoying the lion's share of support from the crowd, broke in the next game to seal the set 6-3.

The 20-time Grand Slam champion said he had remained calm and tried to stay positive after the Thiem defeat.

"There's no reason to be too down on yourself," he said. "We came here to play three matches and give it all we have. It was the big goal of the season to come here and qualify which we did, plus I had a day off."

"Not everything was bad (in the Thiem match) but of course if you over-analyse it, all of a sudden it can be," he added. "I was ready, I was prepared today and that's what matters the most."

Djokovic and Thiem hope to take a major step towards qualifying for the semi-finals when they meet in the later match at the O2 Arena.

Djokovic is hunting a sixth ATP Finals title to pull level with Federer's record and is also seeking to pip Rafael Nadal to the year-end number one ranking.

On Monday, top seed Nadal lost his opener in Group Andre Agassi to defending champion Alexander Zverev while Stefanos Tsitsipas beat Daniil Medvedev. The top two players from each group qualify for the semi-finals.

Copyright Agence France-Presse, 2019