"As we gather here, on this historic property, amidst the bunting and the flags, I'm reminded of a day more than 50 years ago, when I first arrived in the United States," she said in a speech before greeting each of the new citizens from countries including Iran, China and Russia.
"For this priceless opportunity and all that has since come with it, I will forever be grateful, Albright said. "And of course, it never occurred to me that I would be secretary of state and have Thomas Jefferson's job." Jefferson served as secretary of state in President Washington's Cabinet.
A holiday tradition
The ceremony has become a Fourth of July tradition. Across the United States on Tuesday, hundreds of immigrants took the oath and claimed a new home.
Already this year, 375,000 immigrants have become U.S. citizens.
Some, like Jesus Renzoli of Cuba and Biao Sun of China, are leaving communist regimes. "The freedom -- democracy -- you know, this is quite different than where I come from," said Biao.
Renzoli echoed Biao: "I can freely speak about my thoughts, about my feelings, about everything."
They were among immigrants from 40 different countries to take the oath. Albright joined them in pledging allegiance to the United States, "absolutely and entirely ... without any mental reservation."
'I will forever be grateful'
Albright's father was a Czech diplomat who snatched her and her mother, brother and sister from their homeland because of Hitler's Nazi forces, but left his country for good only after he learned he was on a communist death list.
"I was 11, and I do remember being very excited, but also a little scared, because I did not know whether I would be accepted in this new land," Albright said.
"I should not have worried. ... We were welcomed, given refuge and provided the chance to make new friends and build new lives in freedom. For this priceless opportunity, and all that has since come with it, I will forever be grateful."
Albright became a U.S. citizen in her second year at college, at Denver in 1957. "I wanted so much to be an American," she said.
Albright was the first secretary of state to deliver the annual address at Monticello, where Jefferson built the home of his dreams.
She told reporters at a reception afterward of her "awe" of Jefferson, the man most associated with U.S. ideals set out in the preamble to the 1776 Declaration of Independence that "all men are created equal" and with the right to "life, liberty and the pursuit of happiness."
"I always do truly think about the fact that I have Thomas Jefferson's job," Albright said. "That is the part that always undoes me, because it is so hard to comprehend."
Albright said the United States has been "enriched by the steady flow of mind and muscle, culture and creativity" of immigrants from around the world, whose number remained near 6 million a year in the 1980s.
She said she had told the new citizens, as she handed them their certificates, that hers looked exactly the same.
"They were kind of undone by that fact," she laughed.
Correspondent Kathleen Koch and Reuters contributed to this report.