The visiting Minister expressed his satisfaction with the talks, adding that he had enjoyed his stay here.

【翻译】来访的部长对会谈表示满意，并补充说他在这里过得很愉快。

1. his satisfaction with the talks： with 表示“涉及；关于”，作 satisfaction 的定语。其意思跟 be satisfied with...结构的 with 相同。

词组 his satisfaction with the talks 意思上，可以转换成一个“主谓句” ：He was satisfied with the talks. 

2. adding 是现在分词“补充说”，adding that he had enjoyed his stay here，为现在分词短语作伴随状语。