Thefirst daughter is due to lead a US delegation on a trip to the Global Entrepreneurship Summit in Hyderabad next week, which will be her highest profile moment representing the United States so far.
She is attending at the invitation of Narendra Modi, the Indian prime minister, and intends to promote backing for women in business.
But the visit became a catalyst for growing tensions between the White House and Mr Tillerson, who was said to be against “bolstering” Ms Trump’s position on the world stage,CNN reported.
White House officials were said to have privately accused Mr Tillerson, America’s top diplomat, of failing to support Ms Trump.
He was said to feel that Ms Trump and her husband Jared Kushner, both senior advisers to President Donald Trump, had “stepped all over” him during the first 10 months of the Trump administration.
The entrepreneurship summit was attended in previous years by President Barack Obama and his Secretary of State John Kerry.
This year the State Department is sending no official higher than the level of deputy assistant secretary.
Mr Tillerson was said to have insisted that only he and his top staff could approve even the smallest details of the travel plan.
“They won’t send someone senior because they don’t want to bolster Ivanka,” a senior State Department official told CNN. “It’s now another rift between the White House and State Department at a time when Rex Tillerson doesn’t need any more problems with the president.”
A State Department spokesman said: “The Department is committed to supporting women’s economic empowerment and entrepreneurship, and the summit is a prime opportunity to showcase the importance of these themes.”
The row came as Mr Tillerson came under fire from disgruntled officials in his own department.
According to the New York Times he refused to meet the State Department’s chief of security for nine months despite repeated and urgent requests, and then saw him for only five minutes.
Mr Tillerson, the former former chief executive of Exxon Mobil, has made clear his intention to cut bureaucracy in the department but critics have accused him of leaving a diplomatic “vacuum” with many posts unfilled.
In recent weeks Democrats on the House Foreign Relations Committee accused him of presiding over an “intentional hollowing-out of our senior diplomatic ranks” including an “exodus of more than 100 senior Foreign Service officers”