Amazon has touched off a bidding war among cities seeking its second headquarters. (Jim Young/Bloomberg News)

Maryland’s transportation chief said Tuesday that he has promised Amazon a “blank check” for any transportation improvements the retail giant would want if it chooses the state’s Washington suburbs for a second headquarters.

Transportation Secretary Pete K. Rahn said that amount “could be more or could be less” than the $2 billion in unspecified transportation upgrades the state has already committed to as part of its $5 billion pitch for Amazon to choose the White Flint area of North Bethesda in Montgomery County.

“Our statement for HQ2 is we’ll provide whatever is necessary to Amazon when they need it,” Rahn told state senators during a hearing on his department’s budget, according to an online video archive of the public meeting. “For all practical purposes, it’s a blank check.”

Rahn said the state doesn’t have the $2 billion budgeted, saying, “I don’t know how we’d do it.”

“However, there is no doubt we will have to fund it if they choose Maryland, and quite honestly, that would be a problem I would love to have,” he added.

Rahn said the 50,000 jobs that Amazon has pledged “would have massive positive” impacts on the state, though he added there also would be “some negative impacts,” such as traffic congestion.

(Amazon founder Jeffrey P. Bezos also owns The Washington Post.)

Rahn’s comments drew criticism from at least one state lawmaker, who said he found them “jarring.”

State Sen. Bill Ferguson (D-Baltimore City) said he’s worried about how much the state is willing to spend to land the company.

“Having Amazon come to Maryland would be a benefit to the state, but there is a cost analysis that has to be done,” Ferguson said after the hearing. “Any benefit provided has an opportunity cost. A blank check to a private entity seems ill-advised for the long-term success of all of Maryland’s residents.”

Erin Henson, a spokeswoman for Rahn, said he was merely reiterating previous statements “that the state is going to do what it takes to close the deal with Amazon, which includes transportation improvements.” Asked about Ferguson saying he found the “blank check” statement “jarring,” Henson said, “The real news here is that Senator Ferguson is so easily jarred.”

The North Bethesda site is one of 20 regions that Amazon recently announced as finalists in its search. Rahn told lawmakers he didn’t know when the state will hear if its site makes the shortlist, citing a confidentiality agreement it signed with Amazon as part of its pitch.