The world number two continued his pursuit of a 20th Grand Slam title with a 7-6, 6-3, 6-4 win at the Rod Laver Arena.

Federer, the second seed, made a slow start to the match as Berdych, who lost last year's Wimbledon semi-final to the Swiss player, seized control.

The Czech 19th seed went 3-0 up and served for the first set at 5-3 before Federer recovered and claimed the opener on a tie-break.

It turned the tide of the contest as Federer found his form and wrapped up what proved to be a convincing win.

The 36-year-old will take on Hyeon Chung in the last four after the South Korean dispatched American Tennys Sandgren 6-4, 7-6, 6-3.

"You don't want to think too far ahead, what if, what if, because I feel that's exactly the moment when you stumble," Federer said.

"That's why I think I was actually very nervous going into this match tonight, and that's why I struggled very early on. 

"I knew the danger of Berdych. 

"Seeing what has happened to so many other top seeds here in the draw, I was a bit wary going into tonight."

In the women's singles, world number one Simona Halep of Romania ousted Karolína Plíšková of the Czech Republic 6-3, 6-2 to reach the last four.

Halep will face Germany's Angelique Kerber after she beat American Madison Keys 6-1, 6-2 in just 51 minutes.

Sandgren had earlier used his post-match press conference to accuse the media of "demonising" and "propaganda" after controversy surrounding his posts on social media.

The world number 97, who was accused of supporting the "alt-right" movement in the United States, refused to take questions on the subject and instead read directly from a prepared statement.

"To write an edgy story, to create sensationalist coverage, there are a few lengths you wouldn't go to to mark me as the man you desperately want me to be," it read.

"You would rather perpetuate propaganda machines instead of researching information from a host of angles and perspectives while being willing to learn, change, and grow. 

"You dehumanise with pen and paper and turn neighbour against neighbour."