"We are... religious like many of you are... We have many things in common," she told a dozen young Emirati women who have attended leadership and other training programmes in the United States.
Working on "the things we have in common" would help build understanding between countries, Bush said.
Bush arrived in Abu Dhabi late Sunday on a Middle East tour that will take in Saudi Arabia, Kuwait and Jordan designed to raise awareness about breast cancer but also to help restore the US image in the region, damaged by the Iraq invasion.
Wearing a pale green pantsuit, Bush said it was important to "reach out to each other" and remove stereotypes.
She listened to the young women sitting around a U-shaped table in an Abu Dhabi hotel speak enthusiastically about their stints in the United States as part of a Middle East Partnership Initiative.
An estimated 25 million women worldwide will be diagnosed with breast cancer over the next 25 years, said a statement released by the US-Middle East partnership, warning that 10 million women could die without a cure.
Breast cancer remains the leading cause of death among women in the United States and in the Middle East, said Laura Bush's chief of staff Anita McBride.
While previously circumspect on international issues, Bush -- a former teacher and librarian -- has traded in her subdued reputation and become increasingly engaged in the diplomatic arena.
Bush also visited a so-called "pink majlis" at a medical centre in Abu Dhabi, where women draped in the traditional long black robes known as abayas and with their heads covered, told of their struggle to beat breast cancer.
The US First Lady said both her mother and grandmother had breast cancer, but added that her mother was alive while her grandmother had not died of breast cancer.
Bush also attended the signing of a memorandum of understanding between the Abu Dhabi Health Authority and Susan G. Komen For the Cure, a Dallas-based organisation, to work together on a breast cancer awareness programme.
In the neighbouring emirate of Dubai, Bush later addressed a business gathering after 11 Dubai-based companies pledged to spread awareness of breast cancer in their environments through joining the partnership.
"Dubai is the economic powerhouse of the Middle East, and as a global city Dubai is acting as a good global citizen," Bush said, flanked by Princess Haya bint al-Hussein, wife of Dubai ruler Sheikh Mohammed bin Rashid al-Maktoum.
The United Arab Emirates and Jordan have joined a US-Middle East Partnership for Breast Cancer Awareness and Research launched last year, while Saudi Arabia is due to join when Bush visits the oil-rich kingdom on Tuesday.
Bush will go to Kuwait on Wednesday, move on to Jordan on Thursday and end her tour the following day.