The phrase "citing national security concerns" is something called a participial clause. They are formed using the present participle, which is nothing more than the so-called "ing" form of a verb, or the past participle, which is also known as the third form of a verb (those are past-tense words like broken, seen, damaged etc.). One very important fact concerning participial clauses to remember is that they don't contain the main verb of a sentence. In other words, they can't have things like wasn't, can't, was, is, past-tense verbs like left, called etc. in them. What they really are are adverbial phrases that modify the main verb of a sentence. For example:
She left the room, crying her eyes out.
In this example, the participle clause crying her eyes out gives us more information about the way she left the room: she left it, crying her eyes out.
Likewise in your example, citing national security concerns is a participle clause that describes the way the United States government called for a full investigation into a hostile bid to buy the American chip stalwart Qualcomm: they did it, citing national security concerns.
Was calling would be the past continuous tense form of its present continuous counterpart is calling. Do you know the difference between the simple past and the past continuous tense? The past continuous tense (formerly known as the past progressive) has to do with actions that happen in the past and are done repeatedly, while the simple past refers to one-off actions which are actions that happen only once. So, the United States government was not repeatedly calling for whatever they were calling for. It was just one instance of calling. There is really no need for the past contentious tense at all.
We could even paraphrase your example like this, which will hopefully make things a bit clearer to understand:
The clash erupted in public on Tuesday after the United States government, while (or while they were in the process of) citing national security concerns, called for a full investigation into a hostile bid to buy the American chip stalwart Qualcomm.