Six-time champion Roger Federer beat Kevin Anderson 6-4 6-3 to secure his place in the semi-finals of the ATP Finals for the 15th time.

Federer’s victory means he tops his group to boost his chances of avoiding world number one Novak Djokovic in the last four in London.

The Swiss, 37, looked out of sorts when he lost his first match on Sunday but bounced back with two successive wins.

South African Anderson had already won two matches to reach the semi-finals.

Top seed Djokovic is already through to the semi-finals and can clinch top spot in his group by beating Marin Cilic on Friday.

Alexander Zverev, John Isner and Cilic are battling for the other semi-final berth.

Meanwhile, Britain’s Jamie Murray and Brazilian partner Bruno Soares completed a clean sweep of wins in their doubles group by beating Henri Kontinen and John Peers 3-6 7-6 (7-3) 10-3.

• Federer v Anderson as it happened
• Standings, results & BBC coverage
• Incentives to play in ATP Cup – Djokovic

Questions were asked about Federer’s form and state of mind after he lost to Kei Nishikori in straight sets on Sunday but he gave himself a chance of reaching the semi-finals by beating Dominic Thiem on Tuesday.

And after Thiem defeated Nishikori earlier on Thursday, the Swiss knew he needed to win only six games to join Wimbledon finalist Anderson in the semi-finals.

“I’m very happy, my first match was tough and I never got going, but with my back against the wall maybe it’s easier for me to play,” said Federer.

“Kevin’s had a great year, but it’s been a fun group and I’m very happy to be in the semis.”

Federer had three break points on Anderson’s formidable serve in the seventh game of the first set and secured the break when the world number six double-faulted.

Surprisingly Federer shanked two shots to lose his serve in the next game but the Swiss broke again to love as Anderson temporarily lost his range.

Federer had to save three break points at 5-4 but held his serve to take the set – much to the delight of the majority of the fans inside the O2 Arena.

The 20-time Grand Slam winner looked back to near his best in the second set, playing nearer the baseline and moving his opponent around.

And Federer went on to get a small measure of revenge for his Wimbledon quarter-final defeat at the hands of Anderson by wrapping up victory in one hour and 16 minutes.

“These round-robin formats are not straightforward, we’re used to it being you lose, you leave, you don’t hang around,” added Federer, who is aiming to win the 100th title of his career.

“Maybe it was difficult for Kevin having already qualified, whereas with Thiem winning it was maybe easier for me.

“But I’m happy I’m still alive and hope I can play a good match the day after tomorrow.”

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World number one Novak Djokovic has backed the new ATP Cup team event, saying it will provide incentives for leading players to take part.

Djokovic appeared with the ATP and Tennis Australia on Thursday to confirm the event will start in January 2020 as a curtain-raiser to the men’s season.

A revamped Davis Cup tournament will take place in November from 2019.

On Wednesday, Djokovic said he thought two rival events within six weeks would not be “good for the sport”.

The 31-year-old Serb said he feared the situation – which he described as “delicate” – could lead to two “average” events.

“I think in the next two years we’ll have both events happening in a very similar format if not the same, six weeks apart,” the 14-time Grand Slam winner said.

“We have the longest season in all sports. We’re just adding events. We kind of have to try to focus on quality rather than quantity.”

“I think creating one event is an ideal scenario and I think outcome for everyone.”

The ATP Cup will have prize money of £11.35m. It will feature 24 nations in six groups of four and up to 750 ranking points will be available for the winners.

Three Australian cities will host the 2020 event, which will run from 3-12 January and lead into the Australian Open, which starts on 20 January.

Meanwhile, the ITF competition will be an 18-team end-of-season event, which will crown the Davis Cup champions.

The controversial proposals to revamp the Davis Cup were backed by national tennis federations in August, although players were not consulted.

Djokovic, who is the ATP Player Council president, said at the launch of the ATP Cup in London that it was an attractive proposal for the players.

“Having ranking points as an option is obviously an incentive for players,” he said.

“We have a lot of incentives and the biggest one, I’m sure, is playing for your country.

“We have the Davis Cup, which has been the most historical team event, and now we have the ATP Cup, which is definitely going to be right up there in terms of the value from the players’ perspective.”

Earlier in the week, Germany’s world number five Alexander Zverev said he felt none of the top players would play in the Davis Cup.

Analysis

Russell Fuller, BBC tennis correspondent

The ATP Cup will almost certainly be an innovative and enjoyable experience, but the fact remains it will go ahead six weeks after the Davis Cup Finals – even though the head of the ATP said that would be “insane”.

What’s more, both events will be very similar in format.

The ATP prize fund is impressive, albeit US$5m less than the money Kosmos is offering for the revamped Davis Cup.

But the ATP can offer the added pull of up to 750 ranking points for members of the winning team at a time of year which suits the players.

November, in contrast, is a terrible time for a team competition as bodies are tired and injuries rife. Kosmos’ founder Gerard Pique wants the Davis Cup to be staged earlier in the year, but ideally needs the co-operation of the ATP.

Talks continue, but unless common ground is found, there remains a major question mark over the long-term sustainability of the Davis Cup.