Britain's biggest business bank has faced severe criticism for mishandling the closure of Farage's accounts with its private bank Coutts, after a dossier emerged showing a bank committee had said his views did not align with the lender's own.
Rose stepped down on Wednesday after admitting to a "serious error of judgment" in discussing Farage's relationship with the bank with a BBC journalist, while Coutts CEO Peter Flavel was ousted a day later.
Davies said he intended to stay on at the bank for now - after also facing calls to resign - and confirmed for the first time that political pressure forced the board's hand in Rose's exit.
"The political reaction to that was such... that her position was then untenable," he told reporters.
"We've lost a great leader," he added.
NatWest is nearly 40% taxpayer-owned following its bailout during the 2008-2009 global financial crisis.
Britain's finance ministry said the decision for Rose to depart was made by her and the bank's board.
"The NatWest board is responsible for the bank's strategic and operational management," a Treasury spokesperson said.
While the government has long described itself as an "arms-length" investor and Davies said it had not interfered in commercial decisions during his eight-year tenure at the bank, he noted the "exceptional circumstances".
He said it would "theoretically" have been possible for Alison to continue despite the government's position, but they had both concluded that "maintaining the position of the bank and her authority in the bank would just be too much of a struggle."
Davies has himself come under pressure, with one top-20 investor telling Reuters on Thursday his position looked increasingly shaky after the board backed Rose on Tuesday evening, only for her to leave hours later.
Government intervention appeared to seal Rose's fate, after sources at the prime minister's office and the finance ministry briefed newspapers late Tuesday evening they were not happy with her remaining in post.
Davies said his plan remained for him to leave in 2024, as announced in April.
"I serve at the behest of shareholders and will continue to do so, it is important there is some stability in the bank," he said on Friday.
NatWest said later on Friday it had appointed the law firm Travers Smith to undertake an independent review into the account closure arrangements at private bank Coutts.
ECONOMIC CRUNCH
NatWest's shares were up around 3% in late-morning trading after the bank earlier on Friday beat analysts' forecasts, reporting a jump of more than a third in first-half pre-tax profit to 3.6 billion pounds ($4.6 billion).
The bank made scant reference to the Farage incident in its earnings release, other than to confirm that former commercial banking boss Paul Thwaite had been promoted to interim CEO for initial 12 months.
Thwaite will be tasked with trying to steady the ship after the damaging Farage episode, at a time when Britain faces an economic crunch from stubborn inflation and a cost-of-living crisis impacting many households.
The lender also announced an interim dividend of 5.5 pence per share and announced a share buyback of up to 500 million pounds for the second half of the year.
But it also warned that tightening mortgage margins and savers shopping around for better deals would eat into its margins this year, and set aside an additional 223 million pounds to cover potentially soured loans.
($1 = 0.7820 pounds)
