In the statement, Pfizer chief executive Ian Read said that the company continued to believe "that our final proposal was compelling and represented full value for AstraZeneca".
"As we said from the start, the pursuit of this transaction was a potential enhancement to our existing strategy. We will continue our focus on the execution of our plans, bringing forth new treatments to meet patients' needs and remaining responsible stewards of our shareholders' capital," he added.
In a statement released after Pfizer's announcement, AstraZeneca said it welcomed the climbdown and would "continue building on the momentum we have already demonstrated as an independent company."
AstraZeneca's U.K.-listed shares had come under pressure following the rejection of last week's offer with investors voicing their disappointment that the company had not pursued a deal with Pfizer.
The AstraZeneca statement also stated that the company had "attractive growth prospects and a rapidly progressing pipeline."
"In the coming months we anticipate positive news flow across our core therapeutic areas, which underpins our confidence in the long-term prospects of the business," the company said.