Straight Path's shares were up 6.4 percent at $118 in pre-market trading, much above the offer price, indicating that investors are expecting a bidding war.
Reuters had earlier reported that Verizon Communications was considering outbidding AT&T.
AT&T had agreed to buy Straight Path, a holder of licenses to wireless spectrum, for $1.25 billion in an all-stock deal on April 10.
The new offer represents a deal value of about $1.31 billion.
AT&T could not immediately be reached for comment, while Verizon declined to comment.
Telecom companies are conducting trials for 5G, the fifth generation of wireless technology that is expected to be significantly faster than current networks.
Millimeter wave spectrum between 30 GHz and 300 GHz is expected to play a large role in 5G networks. Straight Path is one of the largest holders of 28 GHz and 39 GHz millimeter wave spectrum used in mobile communications.
Straight Path said on Tuesday it has notified AT&T of the offer and the telecom company has five days to match or exceed the new bid.