Toto Wolff says McLaren's remarkable gains of late 'give encouragement' to Mercedes that the Brackley squad can also continue to move forward.
McLaren introduced in Austria a three-stage development programme that delivered an impressive performance boost to the Woking-based outfit.
At Silverstone, Lando Norris and Oscar Piastri qualified second and third, and finished respectively second and fourth on race day.
Speaking ahead of next weekend's Hungarian Grand Prix, Wolff noted the continued variation of the running order behind Red Bull, and the presence of McLaren among its direct rivals alongside Aston Martin and Ferrari.
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"At Silverstone, we outscored our closest competitors," said Wolff. "We executed well on race day. We were able to race to the podium and extend our P2 advantage in the championship.
"However, the order is fluctuating almost every weekend. We need to keep adding performance if we are to close the gap to the front and fight for victories.
"Several teams have made big gains recently. This has brought some into the fight with us, especially McLaren.
"It has been impressive and gives us encouragement that we can also continue to find gains. We relish that challenge and will bring our own steps in due course."
Wolff says Mercedes aims to carry the momentum it displayed at Silverstone into Hungary, a venue that has treated the German outfit well in the past.
In 2013, Lewis Hamilton enjoyed in Budapest his first triumph in F1 with Mercedes. Thereafter, the seven-time world champion delivered four more wins to his team.
"The Hungaroring is a circuit that is quite different in nature to Silverstone. It will be interesting to explore how our latest upgrades perform in the long-radius, slow-speed corners," Wolff added.
"We have good memories from Hungary last year, with George's first pole position in F1 and a double podium for the Team.
"This race also marks a decade since Lewis' first win with us, so it's a circuit full of good memories.
"Hopefully we can have another strong showing this time out. We want to build on the positive momentum from Silverstone and take the fight to our rivals."
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