Enterprise said in its statement that movements in its stock price as well as questions from its investors drove it to make the withdrawal publicly.
"While we are disappointed, we will maintain our financial discipline as we pursue future growth opportunities for the partnership," Enterprise Chief Executive Jim Teague said in a statement.
Enterprise Product Partners' initial approach came after peer Energy Transfer Equity walked away from an agreed-upon takeover of Williams in June. Nearly half of Williams' board resigned following a failed attempt to oust the company's Chief Executive Officer Alan Armstrong.
Activist investor Corvex Management, run by Carl Icahn protege Keith Meister, has said that Williams' board and management is entrenched and has not served shareholders well by declining to discuss a deal with Enterprise. He nominated a slate of directors last month to replace all of Williams' board.
Williams shares closed up 81 cents at $31.15 on the New York Stock Exchange. They fell around 2.5 percent in after hours trading.
Enterprise units were up 14 cents at $27.25 on the New York Stock Exchange on Thursday. They were up around 1.7 percent after the bell.