By Michael Wursthorn

Hopes for an eventual infrastructure bill by the Trump administration sent shares of several construction stocks higher Tuesday.

Shares of equipment company United Rentals Inc. jumped 7.7%, while Caterpillar Inc. rose 5.3%. Some smaller construction-related stocks also popped. Summit Materials Inc. climbed 6.2%, U.S. Concrete Inc. went up 23%, Granite Construction Inc. added 16% and Infrastructure & Energy Alternatives Inc. surged 15%.

The advances followed a report ahead of Tuesday's opening bell that the Trump administration is preparing a nearly $1 trillion infrastructure proposal as part of the government's continuing efforts to revive the economy. It wasn't clear when such a plan would be revealed.

A big infrastructure-spending bill has been one of the president's earliest priorities. In 2016, he pushed for a $1 trillion plan to invest in U.S. roads and bridges, only to hit roadblocks. Subsequent efforts have also fizzled out, but the administration plans to use the renewal of an existing infrastructure bill at the end of September as a vehicle to drive its latest effort through, Bloomberg said.

But investors who missed out in the rally might be in luck. Tuesday's moves mirrored days of big gains in those stocks in recent months following comments from President Trump and other government officials on infrastructure spending.

U.S. Concrete, for example, jumped 23% on March 31 after Mr. Trump called on Congress to allocate as much as $2 trillion toward infrastructure in future coronavirus-aid relief packages. Summit Materials rose 20% that day, while Granite Construction and United Rentals added 12% and 8.1%, respectively.

Some of those stocks also got a boost on May 27 after New York Gov. Andrew Cuomo urged the president to speed up major infrastructure projects. U.S. Concrete soared 16% that day, while Summit Materials rose more than 6%.

Even with those gains, some construction stocks continue to trade at attractive valuations. United Rentals shares currently trade at 10 times its trailing 12-month earnings, according to FactSet, while Caterpillar and Infrastructure & Energy Alternatives trade at 14 and 12, respectively. That is well below the S&P 500's price/earnings ratio of 21.

That could leave some stock pickers with further openings to pounce on these stocks as Congress and the White House continue working on an infrastructure plan.

Write to Michael Wursthorn at Michael.Wursthorn@wsj.com