General Motors shares climbed Monday after Deutsche Bank said a meeting with the automaker's management "confirmed" expectations GM could launch self-driving vehicles "well ahead of competitors."

Shares of GM rose more than 4 percent Monday to a record, surpassing a previous high from December 2013.

"GM confirmed that their [autonomous vehicles] are on track for a critical milestone… they will be safely driving passengers in complex urban environments without a human backup driver within the next few quarters, well ahead of competitors," research analyst Rod Lache and a team of other analysts said in a Sunday report. "GM agreed with our suggestion that large scale commercial operations would start relatively soon (we expect this in 2020)."

The conversations with GM management also indicated the company plans to launch its own transportation service to compete with Lyft and Uber, Lache said. "GM does not intend to sell the technology to unaffiliated third parties; and GM appears to have thought through many details of how the [Transportation as a Service] will operate," he said.

GM declined to comment on the report and referred CNBC to its second quarter analyst call in which Chairman and CEO Mary Barra said the company is investing in "transformative technologies" such as electrification, autonomous technology and connectivity.

Separately, GM said Monday that it is planning to roll out two new electric vehicles in the next 18 months, for a total of up to 20 all-electric vehicles over the next six years.

Lache also expects GM's autonomous vehicle operations will first launch in the "most lucrative markets" of densely populated cities at a cost of less than $1 per mile.

Last Sunday, Sept. 24, Lache upgraded GM's shares to buy from hold and said that he expects "GM's [autonomous vehicles] will be ready for commercial deployment, without human drivers, much sooner than widely expected (within quarters, not years); that businesses built off of this platform will ramp much faster than is widely expected; and that this will be material, even to a company of GM's size."

"Our takeaway from this meeting [with GM management] was that our key conclusions were spot on," Lache said in his latest report.

GM shares have risen more than 7 percent from the close on Friday, Sept. 22, through Monday morning trading. The stock is up 21 percent for the year.

Shares of electric car maker Tesla, which many see as leading the future of automobile development, recovered intraday losses to close 0.13 percent higher Monday. The stock is up nearly 60 percent this year.

As of Friday's close, GM had a market capitalization of about $61.5 billion, recovering its lead on Tesla's market cap of $56.5 billion after falling below Elon Musk's company in April.

— CNBC's Tae Kim contributed to this report.