UPDATE 1-U.S. Senate's McConnell tells Yellen Democrats must raise debt ceiling themselves

(Adds comments from McConnell's office, background on debt ceiling)

WASHINGTON, Sept 16 (Reuters) - Mitch McConnell, the Senate's top Republican, has told Treasury Secretary Janet Yellen that congressional Democrats will have to raise the U.S. debt ceiling on their own, even as she warns of a default and new financial crisis if lawmakers do not raise the federal borrowing limit.

McConnell spokesman Doug Andres said on Thursday the Senate Republican leader in a telephone conversation a day earlier "repeated to Secretary Yellen what he has said publicly since July: This is a unified Democrat government, engaging in a partisan reckless tax and spending spree. They will have to raise the debt ceiling on their own and they have the tools to do it."

President Joe Biden's fellow Democrats narrowly control both the Senate and House of Representatives. If Congress fails to raise the $28.5 trillion debt limit, it could lead the government to default on its payment obligations.

Yellen said this month that cash and "extraordinary measures" being used to finance the U.S. government temporarily will be "exhausted" during October.

McConnell and other senior congressional Republicans have vowed not to vote for an increase of the debt limit, instead urging Democrats to pass it on their own through a maneuver called reconciliation. McConnell has sought to block numerous parts of Biden's legislative agenda.

House Speaker Nancy Pelosi has said Democrats will not include a provision to raise the borrowing limit in a $3.5 trillion "reconciliation" spending measure they hope to pass this autumn.

Pelosi says the debt limit must be raised to pay for debt incurred under Republican former President Donald Trump, but has not said how this should be done. One possibility would be for Democrats to add a debt ceiling provision to a must-pass bill to keep the government running, expected at the end of September.

Yellen has told lawmakers that a default on U.S. debt obligations would be "unthinkable" https://www.reuters.com/article/us-usa-treasury-yellen/yellen-warns-congress-of-unthinkable-u-s-default-risk-without-debt-limit-hike-idUSKCN2DZ2ET and "would have absolutely catastrophic economic consequences." She has said that the majority of the debt had accrued prior to the Biden administration and that Republicans and Democrats had previously worked together multiple times to address the borrowing issue.

(Reporting by Susan Cornwell; Editing by Will Dunham)