He was brought up in the Netherlands, at Leiden, attending the university there. He was in Cologne, at the Walloon Church, 1624-6, and subsequently at Elbląg (Elbing). He was a close associate of Samuel Hartlib, a native of Elbląg, whom he met there, and shared his interest in education. According to Richard Popkin , another key influence was Joseph Mede, from whom Dury took a method of scriptural interpretation.
From 1628 he petitioned Gustavus Adolphus for help in the cause of Protestant unity. He spent much time wandering Europe. He met Comenius, who, spent some years in Elbląg as well, with an introduction from Hartlib.
Up to 1633, he had Anglican support from George Abbot. In that year, Abbot died and was replaced by William Laud, with whom Dury had a much more difficult relationship; Christopher Hill states Laud had no use for the efforts of Comenius, Dury and Hartlib to reunite Protestants. He was ordained in 1634, and went to Sweden, supported by 38 English Puritans. The networking of Dury and Hartlib in the 1630s brought them close to Oliver Cromwell, through Oliver St John (a relation by marriage, and friend) and the Godmanchester preacher Walter Welles, a neighbour.
He then travelled widely in northern Europe, and was tutor to Mary, Princess of Orange in the Hague. He had a long though unproductive meeting with René Descartes in 1635; also in the Netherlands he was an associate of Adam Boreel and Petrus Serrarius, and an influential figure.
In 1645, Dury and Comenius came to England; an invitation had been mooted in a sermon by John Gauden in 1641, at the start of the Long Parliament. Dury gave a well-known sermon to the Parliament on 26 November 1645, Israels Call to March out of Babylon into Jerusalem. He was given an official appointment, as tutor to the younger children of Charles I; from 1646 these had been in the care of Algernon Percy, 10th Earl of Northumberland.
After the war in England had ended, he argued both for religious toleration, and for acceptance of the Parliamentarian regime. He incurred the displeasure of the Westminster Assembly, to which he belonged, for his part in the 1648 publication (with Hartlib and John Goodwin) in translation of part the theological work Satanae Strategemata of Jacob Acontius on toleration. He called on the Ranter Abiezer Coppe to repent, and helped in drafting his recantation. He provided arguments in pamphlets of March and October 1649 for supporting the Rump Parliament. Hill places Dury with Anthony Ascham and Marchamont Nedham as propounding the theory that Parliament had legitimacy conferred by God because it held power de facto. Barbara Lewalski calls Dury's arguments 'Hobbesian'. Hill considers that the failure of Cromwell's plan to create a unified Protestant church in England of the 1650s put paid to Dury's ecumenical ideas.
In 1652 he translated John Milton's Eikonoklastes into French as Eikonoklastēs, ou, Réponse au livre intitulé Eikon basilikē. In 1655 Milton quoted from letters of Dury in his Pro se defensio contra Alexandrum Morum.
In 1654 he was sent as a diplomat by Oliver Cromwell to Germany, the Netherlands and Switzerland. In 1652/3 he had travelled with Bulstrode Whitelocke to Sweden.
He also worked with Whitelocke as a deputy librarian, from 1649, of the collection going back to Jane Lumley. His book of 1650 on librarianship, sometimes said to be the first such work, came out of his experience in this post..
He met Manasseh ben Israel in 1644, and heard from him an account of Antonio de Montesinos's alleged discovery of the Ten Tribes in America. In 1649 he addressed a further inquiry to Manasseh on the subject, which resulted in the publication of The Hope of Israel. In 1650 appeared Thomas Thorowgood's Jewes in America; Dury read it in manuscript, and contributed to later editions. A year or so before, Dury had written in favour of a Hartlib Circle project, for a College of Jewish Studies. Parliament was lobbied for funds.
Dury is considered to have been one of those around Cromwell influencing the decision to allow Jews to enter England officially (they were expelled by Edward I).. His millennarian views pointed to 1655 as apocalyptic. He was the cautious author of a pamphlet of 1656, A Case of Conscience: Whether It Be Lawful to Admit Jews into a Christian Commonwealth. To a question put to him by Hartlib, as to the general lawfulness of their admission, Dury replied in the affirmative; but from the point of view of expediency he considered that circumstances as to a particular time and place might render their admission unwise. He took a particular interest in the Karaites .
Dury's long ecumenical efforts have earned him a name as an irenicist. This territory he shared, to an extent, with his contemporary Hugo Grotius. Dury made contact with Grotius through his follower Samson Johnson (1603-1661). That relationship soured, since Dury had a hand in Johnson's dismissal as chaplain to Elizabeth, Queen of Bohemia, suspected of Socinianism. According to Trevor-Roper,
Young writes:
At its nexus, it was an association of personal friends. Hartlib and Dury were the two key figures: Comenius, despite their best efforts, always remained a cause they were supporting rather than a fellow co-ordinator. Around them were Hübner, Haak, Pell, Moriaen, Rulise, Hotton and Appelius, later to be joined by Sadler, Culpeper, Worsley, Boyle and Clodius. But as soon as one looks any further than this from the centre, the lines of communication begin to branch and cross, threading their way into the entire intellectual community of Europe and America. It is a circle with a definable centre but an almost infinitely extendable periphery.
Alchemy was within the interests of the Hartlibian group, and both Dury and his wife were involved. In 1649 they were quizzing Worsley on distillation. In the first half of 1651 Dury was a witness to George Starkey, in an apparent transmutation, and then recommended Starkey to Moriaen.
Their daughter Dora Katherina Dury (1654-77) was Henry Oldenburg's second wife.