(My Japanese and my linguistics are both pretty rusty, so grammar geeks may want to correct some of the details in comments.)
The sentence is simpler than it looks. A literal translation (often a good step on the way toward an idiomatic one) would be something like:
As for the six countries such as America and Europe, thinking “might not Iran be trying to make a nuclear weapon?”, they were continuing the sanctions (i.e., the prohibition on trading and such).
Breaking it down:
- 「ＡやＢなど」is a construction meaning “A, B, and so on” or “such as A and B”.
- 「6つの国」is “six countries” or “the six countries”. (Personally I would have stuck another の in there to join the two noun phrases,「アメリカやヨーロッパなどの6つの国」, but I'm not a native speaker.)
- 「は」(“As for…” in the heavy-handed literal translation) is the topic marker, as of course you know.
- 「イランが核兵器をつくる」would be “Iran makes nuclear weapons” or “Iran makes a nuclear weapon.” 「つくろうとする」would be “tries to make”, so「つくろうとしている」gives us “is trying to make.”
- 「の」here turns the preceding clause this into a noun phrase (similar to こと, see below), which we could render in English as “Iran's attempt to make a nuclear weapon”, but in context it's closer to “that Iran is trying to make a nuclear weapon”, or even “the fact that Iran is trying to make a nuclear weapon”. I say “fact,” but—
- —the「ではないか」casts doubt on that (it's equivalent to「じゃないか？」). “Might it not be the case that Iran is trying to make a nuclear weapon?”
- The「と」here is the quotative「と」(you can tell because it's followed by「考える」, just as if it were「思う」or, what you're most likely to encounter first when studying Japanese,「言う」), indicating that the whole preceding phrase about Iran is what the six countries are thinking. (Thus the heavy-handed quotation marks in my literal translation.)
- The verb「考える」is in what's called the gerund form here, 「考えて」— “thinking”.
- I've translated 「続けていました」 literally as “they were continuing”, but as discussed in this answer the ～ている form indicates the continuation of a state as well as the continuation of an action. Just “continued the sanctions” is probably closer. (It's extra-confusing because we're dealing with the verb「続ける」, ‘continue’. “Continued to continue” would be over the top as a translation, but that sort of implication is probably in there. An English-language article would probably say something like “agreed—” or decided, or determined— “to leave the sanctions in place.”)
- Backtracking: as before, ～など means “such as” or “etc.”「こと」(事) literally means “thing” or “fact”, but here it just acts to turn「禁止する」into a noun phrase—“the prohibition of”.
All that gives us:
The six nations—America, Europe, and so on—suspecting Iran might [still] be trying to make a nuclear weapon, continued the sanctions (i.e. prohibition of trade and such).
When in doubt, work backwards. 考えて, ～と考えて, ～か, ～ないか, ～ではないか… if you start from the verb you're much less likely to accidentally invent new particles like かと and ので.
I hope that helps!