UPDATE 2-Qwest pulls network sale after low bids

* Qwest says network more valuable to shareholders

* Shares falls 4 pct in early trading (Recasts first paragraph, changes sources, adds background)

NEW YORK, June 8 (Reuters) - Qwest Communications International Inc (Q.N) said on Monday it pulled the sale of its long-distance phone network after failing to attract a sufficient bid.

The phone company's move added to investors' worries about the company's debt woes and sent shares 4 percent lower.

Qwest said the phone network asset holds far more value to its shareholders and is more strategically important to the company.

It asked for bids over $2 billion last month according to people familiar with the bids.

These people said companies including Level 3 Communications Inc (LVLT.O), and tw telecom inc (TWTC.O) were expected to bid for the assets, potentially in partnership with private equity investors.

Larger phone companies including Verizon Communications Inc (VZ.N) and AT&T Inc (T.N) have also looked at the network but would be interested only if they could get it cheap.

The sale comes as Qwest has been struggling to pare down its debt ever since the technology bubble burst earlier in the decade. Its chief financial officer said earlier this year that the company has $560 million in debt maturing in 2009 and another roughly $2.2 billion due in 2010.

Its vastly rural territory is seen as a disadvantage to building more advanced infrastructure for Internet services, and it has been considered one of the weakest of the former Bell operating companies.

Unlike its bigger rivals like AT&T, it lacks a mobile phone unit to compensate for the decline in its landline business, making it particularly vulnerable as customers disconnecting home phones in favor of cable rivals or wireless services.

Its long distance network serves as a wholesale business, carrying long-distance voice and Internet traffic for other phone carriers.

Qwest also reaffirmed its 2009 outlook, expecting adjusted free cash flow to be $1.4 billion to $1.5 billion and earnings before interest, taxes, depreciation, and amortization of $4.2 billion to $4.4 billion inclusive of pension expenses.

Its shares fell 16 cents to $4.01 in early trading. (Reporting by Yinka Adegoke, editing by Dave Zimmerman and Derek Caney)