The Pakistan-born Khawaja has been in imperious form in his comeback from a 30-month Test exile, hitting 137 in the first innings before adding an unbeaten 101 to break English hearts.

His domineering 179-run partnership with youngster Cameron Green set up a late declaration and left a beleaguered England having to defy history with a formidable target of 388.

The tourists got to the close without losing a wicket for 30, with Zak Crawley on 22 not out and Haseeb Hameed on eight. They trail by 357.

The highest winning run chase in the fourth innings at the Sydney Cricket Ground stands at 288-2 by Australia against South Africa in 2006. No touring team has gone past 200.

England, who surrendered the Ashes inside 12 days and have yet to pass 300 in the series, will hope to stop Australia going 4-0 up on Sunday's final day.

Khawaja became the third Australian player to score twin centuries in 140 years of Ashes cricket at the SCG, and the sixth in a Test match.

"I always wanted to score a century in both innings in first-class cricket and have never done it, but it's just a nice one to tick off," Khawaja said.

"It puts the team in a position where hopefully we can try win a Test match tomorrow. It all worked out pretty well, it doesn't always happen in life, in cricket, it's special."

He toyed with the England bowling with his hundred flowing off 138 balls, laced with 10 fours and two sixes.

He had solid support from Green, who registered his second Test half-century with a confidence-boosting 74 before he top-edged Jack Leach to Joe Root.

Alex Carey surprisingly came out to bat and was out first ball to Leach, signalling the long-awaited declaration by skipper Pat Cummins.

Leach finished with 4-84 off 21.5 overs.

Khawaja and Green rebuffed England's efforts after the loss of key batsmen David Warner, Marnus Labuschagne and Steve Smith to have the Australians at 86 for four.

Smith again failed to get going in a 31-ball stay and was bowled for 23 after he was late on the shot from a Leach skidder.

So far in the series, Smith has scored a total of 217 runs after scoring 93 in the second Adelaide Test. His series average stands at 36.16, well below his current Test average of 60.84.

Mark Wood once again captured the valued wicket of the number-one-rated Test batsman Labuschagne, having him caught behind for 29.

The Durham express bowler has now taken Labuschagne's wicket three times among his eight wickets in the series, in the space of 52 balls.

Australia lost openers Warner (3) and Marcus Harris (27) before lunch.

The indefatigable Wood coaxed an outside edge off Warner for stand-in wicketkeeper Ollie Pope to take the catch.

Pope finished with four catches deputising for Jos Buttler, who had X-rays after taking a blow to his left index finger on day two.

Buttler's injury will be evaluated at the end of the Sydney Test, team officials said.

The stand-in gloved a catch to dismiss Harris off spinner Leach.

England earlier added 36 runs before they were dismissed for 294 to give Australia a 122-run innings lead.

Jonny Bairstow added 10 more runs before he was caught behind off Scott Boland.

The big Yorkshireman soaked up the crowd's applause as he left the field, after his first Ashes century in Australia.

Bairstow faced 158 balls and hit eight fours and three sixes, battling on after taking a nasty blow to his thumb from Cummins when he was on 60.

Boland continued his remarkable series with his team's best figures of 4-36.

Since his extraordinary Test debut in Melbourne, where he was man of the match with 6-7, he has captured 11 wickets at 8.27.