"We think we have the biggest truck month in history. The statistics will tell the story when they are released...We think it is an absolute all-time U.S. record for any manufacturer, any month for full-size trucks — pickups and SUVs," he told reporters after addressing a business lunch.
U.S. car industry sales data are due later on Friday.
Lutz also said he did not expect sales of sport utility vehicles to suffer as long as U.S. gasoline prices stayed under $3 a gallon.
"The demise of the full-size truck is a figment of the imagination of the popular press. Everybody assumes it is true but the market is still buying," he said.
U.S. average retail gasoline prices are up 29.4 cents from a year ago at $2.215 a gallon, according to the Energy Information Administration's (search) weekly survey released on Monday.
Lutz declined comment on prospects for extending past July 5 a U.S. programme that gives all customers the same steep discounts that GM staff get, or on prospects for wringing concessions on healthcare costs from its unionised labour force.
GM, which posted a $1.1 billion first-quarter loss and saw its debt rating cut to high-yield or "junk" status, has said it urgently needs to slash spending on health care, expected to total nearly $6 billion this year.
Lutz brushed off pessimism about GM's prospects in the intensely competitive U.S. market.
"Nothing is wrong with GM North America that a very appealing product that customers absolutely want to buy — as opposed to us having to sell it with a rebate — wouldn't fix," he said in a speech to the Swiss-American Chamber of Commerce.
The challenge, he said, was to "create a product that we can sell without a $4,000 rebate, which is destroying our margins."