The sale by Sotheby's, which continued yesterday, had been expected to net Mrs Danowski pounds 6m, but valuable works by Cezanne and Degas failed to reach their reserve prices.
A long-running legal battle with the Henry Moore Foundation, which owns most of her father's prodigious output, has left Mrs Danowski with a stack of lawyers' bills. Last year she lost a claim to 215 bronze sculptures worth pounds 100m in the foundation's collection.
Mary Spencer Moore Danowski, 50, an only child and married to an American art dealer, was given many works by her father. The pieces auctioned in New York were from her personal collection and family trusts.
The classic piece Reclining Figure - Bone Skirt, acquired by a private collector for pounds 1.36m, is a monumental carving in travertine marble dating from 1978. At the time Moore was spending the summers at a villa he had built near the Carrara quarries in Italy.
Moore's hero, Michelangelo, had worked with Carrara marble centuries before. The 69in- long figure is one of an acclaimed series exemplifying an observation Moore made in 1931: "The human figure is what interests me deeply, but I have found principles of form and rhythm from the study of natural objects such as pebbles, rocks, bones, trees, plants ... bones have marvellous structural strength and hard tenseness of form, subtle transition of one shape into the next..."
Two other works from the artists collection sold on Tuesday were Jean- Francois Millet's La Baratteuse in black chalk on paper, bought by a dealer for pounds 189,100, and George Seurat's Les Deaux Charrettes, bought by a private collector for pounds 192,510.
Moore belonged to a group of major artists who were also distinguished collectors in their own right. Two works, however, fell short of Mrs Danowski's aspirations. The Trois Baigneuses from Paul Cezanne's bathers series carried a tag of pounds 1m to pounds 1.3m, but was not sold. Nor was a pastel by Edgar Degas of a woman combing her hair which had been estimated at between pounds 310,000 and pounds 434,000.
Mrs Danowski helped to set up the foundation in 1977 to ease Moore's pounds 1m-a year tax bills. When he died, aged 88, in 1986, the foundation owned 669 of his sculptures and thousands of drawings. But Mrs Danowski, in her unsuccessful law suit, claimed that bronzes made between 1977 and her father's death were part of the family estate.
Literature accompanying the sale dwelt on a happier time with the young Mary learning by the artist's side at their Hoglands home in Hertfordshire. "He was the most tremendous teacher," she recalled. "He would use a Vuillard or a piece of African sculpture to make a visual point ... Every second of his life he was refining three- dimensional form."