Leap Wireless International, the prepaid cellphone service provider, said yesterday that its board had rejected an unsolicited takeover offer from MetroPCS.

MetroPCS, another prepaid service provider, offered on Sept. 4 to buy Leap in an all-stock deal that would almost double its customer rolls and expand its reach throughout the country. But since MetroPCS’s announcement, Leap’s stock has traded above the offer price, indicating that investors expect a higher offer.

In a letter to the chairman and chief executive of MetroPCS, the chief executive of Leap, S. Douglas Hutcheson, said that the takeover offer undervalued Leap’s revenue and growth prospects.

MetroPCS has offered to pay 2.75 of its own shares for every share of Leap’s, or about $69.05 based on MetroPCS’s Friday closing stock price. Leap shares closed at $74.32 on Friday.

Mr. Hutcheson also criticized what he said was MetroPCS’s lack of consultation with Leap before it made its takeover offer public, saying that Leap had previously broached the idea of a merger or collaboration in wireless spectrum auctions. Among his concerns, he said, is MetroPCS’s lack of an integration plan in its offer announcement.

“We’re concerned about this unrealistic process they have chosen,” he said.

Both companies offer prepaid service without credit checks.