Whether the works team can be a consistent threat over the course of the 19-race Formula One championship, after being off the pace for much of 2012 and finishing fifth overall, remains to be seen.
"Mercedes have recorded some head-turning times with the programme they have been operating to," Horner, whose own team will start as favourites for fourth successive constructors' and drivers' titles with triple champion Sebastian Vettel, told reporters on Wednesday.
"Their car looks quick, and with Lewis joining the team they will naturally take a step forward. He is worth lap time, which is why they signed him.
"I'm sure they're going to be a factor this season. Their challenge will be sustaining it over the whole season as they've been quick the last couple of years at the beginning - winning the third race in China last year."
Hamilton has joined Mercedes from McLaren, the team that backed him through his teenage years and gave him a sensational F1 debut in 2007 before his 2008 title year, in place of retired seven-times world champion Michael Schumacher.
The 28-year-old Briton and his German team mate Nico Rosberg were fastest on the final two days of testing in Barcelona last weekend with laps quicker than both the race lap record and the 2012 pole position time.
Testing times can be misleading, however, with some teams lapping with heavier fuel loads than others and working to different programmes.
"Lewis, as we all know, is a world-class driver, and he is going to raise their level, and they will be a factor this year," said Horner.
Red Bull were fastest on only one day of testing, with Australian Mark Webber, but Horner was not concerned.
"The one thing we've learned about the testing is it is genuinely impossible to read form," he declared.
"It's been a positive pre-season for us, and it's only when we get to Melbourne we'll see everybody do their bit on Saturday afternoon, and we'll have the first glimpse of what the pecking order is.
"But this year is going to be a massive development race from Melbourne to Brazil, with the added challenge being that we not only have to develop the current car, but also research and design a completely new car for 2014."
The season starting in Australia on March 17 is the last with the V8 engines before the introduction of a new V6 turbocharged unit with energy recovery systems.
Big budget contenders like Red Bull, McLaren, Ferrari and Mercedes have separate teams working on the development of this year's car and design of the 2014 one.
Horner felt Red Bull were under less pressure than success-starved rivals but would not lose their focus.
"There is a real determination within the team to keep this run of success going, to do our very best to defend both of those titles this year," he said.
"We have won three double world championships, they're in the history books now. Nobody can take them away from us. We're not a flash in the pan as people thought of us after our first double championship.
"So in many respects the pressure in certain ways is off, but in others we want to keep the roll that we have been on over the past few years continuing this year and beyond."
- Sports & Recreation
- Motor Racing