By Rupam Jain Nair and Douglas Busvine

NEW DELHI (Reuters) - India's evacuation of nearly 4,000 nationals from Yemen has been a triumph of improvisation, but some officials in Prime Minister Narendra Modi's government say a slow response to the crisis has underlined the need for a full-time staff to protect Indians abroad.

On Monday, India rescued more than 1,000 people by plane and ship, the most on a single day since Saudi Arabia launched air strikes against Iran-allied Houthi rebels in Yemen on March 26. India has been asked by 26 nations - including the United States - to help get their citizens out of the conflict zone.

Yet New Delhi struggled for several days to ramp up its rescue effort and had to hire a ship to make the first evacuation of its nationals from the port of Aden as fighting escalated there.

Government insiders draw unfavourable comparisons with China's swifter evacuation of 570 nationals on warships that was completed on March 31. An Indian navy patrol vessel was only able to go in on the following day.

"The Chinese were way ahead in the rescue process," said one senior foreign ministry official, requesting anonymity due to the sensitivity of the matter.

India's rescue effort got off to a false start, with planes commandeered from Air India [AIN.UL] sitting idle in Muscat, Oman, because it was impossible to negotiate the opening of a safe air corridor with the Saudis.

Things only really got moving with the deployment of foreign office minister V.K. Singh - a retired army chief - to a forward operations base in Djibouti, across the Gulf of Aden, from where air force C-17 transporters have picked up evacuees brought out by Air India from Sanaa and flown them home.

A second official said the challenges of evacuating thousands of Indian nationals from fighting in Iraq last year had shown that a full-time staff was needed to rescue overseas Indians in times of crisis.

"We were late in assessing the crisis - and this was exactly the same case during the Iraq crisis," the second official said.

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The scramble jars with Modi's ambition to boost India's global influence, by increasing the military's ability to project power and connecting with a large and widely dispersed diaspora that was long neglected by the government.

The Ministry of External Affairs has, however, rebutted criticism that it was slow to warn more than 4,000 Indians living in Yemen to leave, saying it issued the first of a series of advisories in January as the security situation deteriorated.

Foreign ministry spokesman Syed Akbaruddin declined to comment on calls for a permanent evacuation staff, saying the rescue had gone remarkably well in difficult conditions.

"It was much more perilous, the circumstances were more turbulent, and diplomatically it was a tightrope walk," said Akbaruddin.

India flew 600 nationals out of Sanaa and Tuesday and plans to make its last evacuation flights from the capital on Wednesday, the ministry said. No Indians have been reported killed or wounded in the fighting in Yemen.

FOREIGN ASSETS

There are 21 million people of Indian origin abroad and they send home an estimated $70 billion a year in remittances - more than any other country receives from its overseas workers.

One-fourth of these overseas Indians are in the Middle East, most of them nurses, construction workers, drivers and hotel staff. India evacuated 7,000 citizens from Iraq last year, and nearly 18,000 from Libya in 2011, as fighting swept these nations.

Modi, since sweeping to power last year, has pressed for higher pay for migrant workers in the Gulf and cracked down on private recruiters who charge big up-front fees to place medical staff abroad.

Yet India's embassy in the Yemeni capital Sanaa has a full-time staff of just 10, making it tough to track citizens there - some reluctant to leave even in the face of danger because losing their jobs would spell financial ruin.

Many of those still in Yemen are nurses from Kerala, in southern India. The state's chief minister called on the federal government on Monday to instruct its embassy to intervene to get their passports back from employers so that they can go home.

"There is pressure growing from below," said foreign policy expert C. Raja Mohan, a distinguished fellow at the Observer Research Foundation in New Delhi, who has called for a "well-staffed permanent mechanism" for Indians abroad.

"India needs quite clearly a mechanism that can look at the full spectrum of issues and bring the military in," said Mohan.

(Additional reporting by D. Jose in Thiruvananthapuram; Editing by Robert Birsel)