"in making this assertion" is correct and usable in written English.
You can use it when you are asserting a statement, in order to make a point or explain a situation. For example, "The author appears confident in making this assertion, but a closer examination of the evidence reveals that it is not supported."
The problem now is that Blair was so successful in making this assertion that even many of his critics seem implicitly to accept it.
The assertion that the two can be compatible stems from theology, not science; in making this assertion Dr. Ayala acts as a theologian, not a scientist.
In making this assertion so frequently, we run the risk of sounding like the boy who cried wolf, and therefore not being taken seriously when an election comes around that really is important to American history.
In making this assertion, the commission disputed the view of Mayor Giuliani and top police officials that the disparity merely reflected people who were identified as suspects by crime victims and witnesses.
In making this assertion Zermelo meant to emphasize the fact that in this form the principle makes no appeal to the possibility of making "choices".
In making this latter assertion he is implicitly appealing to geometric intuition, since he makes no attempt to define real numbers, observing only that irrational numbers are to be regarded as the limits of sequences of rational numbers.
In [35, 37] we made this assertion for any finite group G, see however Remark 23.
Given that Eliot made this assertion in 1961, nearly 25 years after In Parenthesis was first published, its remaining a minority interest was already likely.
He repeatedly made this assertion in Amazing Stories, and continued to do so in his editorials for the new magazines, stating, for example, that "teachers encourage the reading of this fiction because they know that it gives the pupil a fundamental knowledge of science and aviation".
Mr. Berezovsky made this assertion in a letter addressed to President Vladimir V. Putin that was made available to news organizations today.
4) "Chinese people are getting richer because they work harder" The health secretary Jeremy Hunt made this assertion in advance of the state visit saying that British people need to work as hard as the Chinese if we want to stay prosperous.
